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Mechanical drawing;
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MECHANICAL DRAWING
WORKING DRAWINGS
BY
ARTHUR B. BABBITT
TEACHER OF MECHANICAL DRAWING, MANUAL TRAINING
DEPARTMENT, HARTFORD, CONN., PUBLIC HIGH SCHOOL
NEW YORK
HENRY HOLT AND COMPANY
1911
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Copyright, 1911
BY
HENRY HOLT AND COMPANY
PREFACE
This book is designed to cover two different fields.
As an elementary textbook it is complete in itself
and should enable the student to make or read any
simple mechanical drawing. As an introductory
work, in schools that offer a three or four years'
course in Mechanical Drawing, it should lay a good
foundation for the subject of Projection.
The drawing instruments are explained as they
_, are introduced in the course, instead of in a chapter
by themselves. Each problem is fully discussed
before the student is expected to attack it. It is
suggested that the student be required to work out
his problem for each plate, freehand, outside of the
classroom. This will give him valuable practice in
^xTft'eehand sketching, and it will save time in the
i classroom for needed attention to technique.
The exercises in lettering (Chapter XIV), should
Jshow results in the improved appearance of all
drawings made. The Geometrical definitions are
usually wanting in books on Mechanical Drawing;
but are inserted here (Chapter XIV). Even if not
set as a lesson to be learned, they will still be found
very useful for reference. The geometrical exercises
p. in Chapter X\TI are accompanied either by a ref
erence to the solution of the problem given in Chap
iv PREFACE
ter XVI, or by the note "original," signifying that
the student is to work out the problem for himself.
The course may be given without homework, but
the author is a firm believer in homework. Where
such work is required, the results immediately aimed
at are better, and in many indirect ways the subject
is found to have a higher educational value. The
author has, therefore, been rather liberal in sugges
tions for outside work, and has added extra plates
for the special benefit of the ambitious student.
The book represents the work of a year, two
fortyfive minute periods a week, and is the result
of a ten years' testing process in the classroom,,
with high school students in the regular course, and
with young machinists in evening classes.
A. B. B.
Hartford, Conn.
Aug. 15, 1911.
CONTENTS
CHAPTER PAGE
I Material 1
II Preparation and Use of Material 7
III Laying out the Sheet 10
IV Use of Instruments 15
V Use of Triangles 24
VI Working Drawings 31
VII Objects with Oblique Surfaces 53
VIII Assembly Drawings 66
IX Use of Instruments 80
X Cylindrical Work 90
XI Scaled Drawings 110
XII Sectional Views 119
XIII Partial Sections 135
APPENDIX
XIV Lettering 153
XV Geometrical Definitions 165
XVI Geometrical Problems 180
XVII Geometrical Exercises 196
INDEX TO PLATES
PAGE
Plate 1 18
Extra Plate 21
Plate 2 29
Plate 3 48
Extra Plate 51
Plate 4 56
Extra Plate 59
Plate 5 61
Plate 6 65
Plate 7 69
Extra Plate 74
Extra Plate 77
Plate 8 82
Extra Plate 86
Extra Plate 88
Plate 9 95
Extra Plate 98
Plate 10 100
Extra Plate 107
Plate 11 112
Extra Plate 117
Plate 12 126
Extra Plate 132
Plate 13 143
Extra Plate 147
CHAPTER I
MATERIAL
An elaborate equipment is not necessary for good
work in mechanical drawing, but serviceable material
which with careful handling will produce accurate
results is required. The list given below covers all
that is needed to solve almost any problem, and is
illustrated fully in Fig. 1.
Drawingboard Ink and pencil erasers
T square Pencilsharpener
Triangle, 30°60° Thumb tacks
Triangle, 45° Bottles of drawing ink, red
Scale and black
Scroll Penholder, writing pens
Pencils, 3H and 6H Set of drafting instruments
Drawingboard — The drawingboard should be
made of soft pine with the left or working edge, the
one against which the head of the T square is rest
ing in. Fig. 1, perfectly straight. Care should be
taken to use the same side of the board each time,
and to have the working edge always at the left.
T square — The T square consists of two parts,
the head and the blade. The head of the square is
shown in contact with the left edge of the board in
2 MECHANICAL DRAWING
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MATERIAL
Fig. 1, with the blade extending across the paper.
The blade is used as the ruhng edge.
30 °60 ° triangle — The angles formed by the edges
of this instrument are 30°, 60°, and
90° as shown in Fig. 2 ; hence the
name, 30°60° triangle. Usually
only one of the angles is used in
referring to this triangle and it is
called either a 30° triangle or a
60° triangle.
45° triangle — This triangle is isos
celes as shown in Fig. 3, having
the equal angles 45° and the third
angle 90°.
Scale — This instrument has U. S.
standard graduations and is used for laying off dimen
sions. It should never be employed as a ruling edge.
Scroll — The scroll is made in several varieties and
is used as a ruHng edge for curves where the
compasses cannot be employed.
Pencils — The degree of hardness
of a drawing pencil is shown by
the number of times the letter H
appears on the wooden covering,
or by the numeral that precedes
the H. The larger the number,
the harder is the pencil.
Erasers — That style in which the pencil eraser is
at one end and the ink eraser at the other is best,
simply because it reduces the number of articles on
the drawing table.
Fig 3
4 MECHANICAL DRAWING
Pencilsharpener — Either a pencil file or block of
sandpaper is necessary for sharpening the lead of
the pencil. The former is preferable.
Thumbtacks — Thumbtacks with small heads
should be selected, as they interfere less with the
movement of the T square.
Drawing ink — An opaque, waterproof ink, one
made especially for the purpose, should be used.
Writing fluids are not suitable.
Penholder — The diameter of the penholder should
be small in order that it may enter the small neck
of the bottle in which drawing ink is usually furnished.
Writing pens — The ball point style of pen is best
for lettering, as it is possible to get lines of approxi
mately the same width whether making horizontal
or vertical strokes.
The set of drafting instruments — While expensive
instruments are not necessary, instruments with
which accurate work may be done are essential.
Should the student decide to purchase a set, the
selection should be intrusted to one having had ex
perience in their use.
A set of instruments complete enough for any
draftsman is shown in Fig. 4.
The compass (A) used for drawing circles and arcs
either with pencil or ink, is shown with the pencil
attachment (B) in place. By loosening the clamp
ing screw (C) the pencil attachment may be removed
and the pen attachment (D) inserted.
The dividers (E) are used for dividing lines into
a given number of equal parts also for transferring
MATERIAL 5
measurements from one part of a drawing to an
other.
The lengthening bar, shown at G, has a projection
at one end to be inserted in the leg of the compass,
and a receptacle at the other end into which either
the pencil or pen attachment may be placed. This
extension is used when circles of large radii are desired.
6 MECHANICAL DRAWING
Two sizes of straightline pens are shown at H,
either of which may be used, the selection being left
to the workman.
Instruments K, L, and M are called bow instru
ments, K being the bow pencil, L the bow pen, and
M the bow dividers. With these instruments small
work may be executed more accurately than with
the larger instruments.
N is a cylindrical tube used for holding leads for
compasses.
CHAPTER II
PREPARATION AND USE OF MATERIAL
The pencils — To do good work, one must keep
all pencils sharp; and to keep pencils sharp requires
constant attention. The 6H pencil is to be sharp
ened at both ends; the 3H should be sharpened at
one end only. To sharpen the pencil, remove the
wood exposing about threeeighths of an inch of the
lead, being careful, however, not to let the knife
edge cut into the graphite. The lead should be
sharpened by using the pencil sharpener or file.
One end of the 6H pencil should be sharpened to an
ordinary round point and the other end to a chisel
point. To sharpen the round point after removing
the wood, pass the lead across the file at the same
time rotate the pencil between the fingers. This
should give a long, conical point, tapering from the
place where the wood meets the lead to the extreme
point, with the end as sharp as a needle. When
sharpening the chisel point, pass the lead across the
file without rotating the pencil, tapering the cut from
the wood to the end and removing the graphite until
onehalf at the end is gone. Repeat this process on
the reverse side of the lead until the point has been
brought to a knife edge. The 3H pencil should be
sharpened to a conical point.
8 MECHANICAL DRAWING
The 3H pencil is used for sketching, for printing,
and for other freehand work. All of the straight line
mechanical work on the drawing should be executed
with the 6H pencil. The round point of the 6H
pencil is used for locating points and the chisel point
for drawing lines, with the flat of the chisel against
the ruling edge. One must early accustom himself
to changing from the round to the chisel point, and
vice versa, for different character of work.
The T square — The T square should always be
used with the head against the left edge of the board,
and the upper edge of the blade should always be
employed as the ruhng edge. All horizontal lines
should be drawn from left to right, with the T square
as a guide. The blade of the square should not be
brought up to the point through which the line is to
be drawn, but should be so placed that there will be a
minute space between the blade and the line after
the line shall have been drawn.
The triangles — For the vertical lines of the draw
ing the 60"" triangle is usually employed, as it
gives a longer ruling edge than the 45° triangle.
When used for vertical lines, the triangle should be
placed on the upper edge of the T square with the
60° angle at the right, as shown in Fig. 6. The
placing of the triangle for 30°, 45°, and 60° lines
will be determined by the direction in which these
lines are to be drawn.
The scale — Keep the scale between the body and
the line upon which the measurement is to be taken,
thus bringing the instrument under the hand. When
PREPARATION AND USE OF MATERIAL 9
laying off dimensions, see that the mark is made
directly opposite the required graduation on the scale.
The eraser — For pencil work use only the pencil
end of the eraser. If this will not do the work, it is
no fault of the eraser but it is because the pencil
lines have been made too heavy. Erase in the di
rection in which the line is drawn and not across the
line. To remove a line, use many light strokes rather
than dig into the paper with a few hard ones. Never
wet the eraser for either pencil or ink erasing. For
erasing inked lines use the ink end of the eraser,
following the directions for erasing pencil lines. Be
fore attempting to erase, be sure that the ink is per
fectly dry.
CHAPTER III
LAYING OUT THE SHEET
Each drawing should be inclosed within a rec
tangle, the lines of which may be called margin lines.
This, in tm^n, should be inclosed in a larger one called
the cutoff rectangle the size of the finished sheet.
The cutoff lines are those upon which the drawing
is trimmed after being taken from the board.
When laying out the margin and cutoff lines,
proceed in the following manner:
1. Tack the paper to the board with the longest
edge parallel with the upper edge of the blade of the
T square. Place the paper nearer the upper than the
lower edge of the board and nearer the left edge
than the right. A good way to stretch the paper
on the board is first to insert a thumbtack in the
upper lefthand corner, then, by passing the hand
across the paper, being careful not to change the
location of the paper on the board, stretch the upper
edge and insert a tack in the upper righthand corner.
Stretching the left vertical edge, place a thumbtack
in the lower lefthand corner. The final stretching
may be accomplished by passing the hand diagonally
across the paper from the upper left to the lower
right, and forcing the last tack into place. Remem
ber that the tacks are thumb tacks and should not
LAYING OUT THE SHEET
11
be driven into the board by hammering with a knife
or T square.
2. Find the center of the sheet by using intersect
ing diagonals from the corners of the paper. See
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point A, Fig. 5. Only that part of the diagonal at
or near the center of. the sheet needs to be drawn.
The T square may be used in getting these lines,
by placing one of the edges of the blade diagonally so
it will intersect opposite corners of the paper.
3. Using the scale, measure five inches up and down
and seven inches to the right and left, locating points.
Most scales are not graduated to the extreme end,
and care should be taken to measure from the point
12
MECHANICAL DRAWING
where the graduations begin and not from the end
of the scale. When locating the points, make a
very small dash directly opposite the required grad
uation on the scale. This mark should be made
with the round end of the 6H pencil, and should be
a very light dash and not a point drilled into the
paper. When using the scale, remember the direc
tions, and keep the instrument under the hand.
Fig. 6
4. With the head of the T square held firmly
against the left edge of the board, and using the upper
edge of the blade as guide, draw, very hghtly, hori
zontal lines through the upper and lower points.
Through the points at left and right draw vertical
lines, using the 60"' triangle as a ruhng edge. When
using the triangle for vertical lines, keep the 60°
angle to the right, as shown in Fig. 6. Unless the
triangle is a large one, it will be necessary to make
LAYING OUT THE SHEET
13
the line in two parts. Use great care to make the
Une continuous, without a perceptible joint.
5. Locate points f ^' above the upper margin line, I"
to the right of the righthand margin hne, I" below
the lower margin hne, and i" to the left of the left
hand margin line.
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6. Through these points draw lines forming the
outer rectangle shown in Fig. 5. These lines form
the finished size of the sheet.
In Figs. 7 and 8 are shown, respectively, the
upper right and lower righthand corners of the draw
ing, giving the lines to be drawn for the printing and
the relation of these lines to the margin lines. The
14 MECHANICAL DRAWING
plates should be numbered consecutively, and each
one should have the draftsman's name and the date
of finishing the drawing.
CHAPTER IV
USE OF INSTRUMENTS
(Straight Line Work)
PLATE 1
SUGGESTIONS FOR PENCILING
Accuracy and neatness are the two essentials
for good work in mechanical drawing. As stated
before, sharp pencils are absolutely necessary to
do accurate work and should be the first things to
receive attention when beginning the lesson. Not
that only once during the lesson should the pencil
be pointed, but one should begin with the tools in
proper condition, and then,^ — keep them in condition.
To do neat work requires clean hands, careful at
tention to details, light lines, and painstaking eras
ing, when erasures are required. Special attention
should be given to the making of light, fine lines, for
heavy lines are a disgrace to any draftsman. Re
member that you are making the drawing on the
paper and not into it. With the hard 6H pencil
it requires no great pressure to cut a line into the
paper that no amount of erasing will remove. One
does not usually err by making the lines too fine and
light. When using the scale, be careful to make the
marks directly opposite the required graduations
16 MECHANICAL DRAWING
and when drawing the lines, see that they go exactly
through the points located. All horizontal hnes
should be drawn from left to right and all vertical
lines from the bottom up. In general, draw the lines
away from the body.
SUGGESTIONS FOK INKING
The straightline or drawingpen — This pen should
be used for inking all straight lines of the drawing
and all curves where the scroll is required for the rul
ing edge. The thumbscrew is for adjusting the
nibs of the pen for the different widths of lines. Care
should be used not to screw this thumbscrew up
too tight, for the threads are very fine and will
easily strip off, thus ruining the pen. To fill the
pen, place the quill — one is usually furnished with
the small bottles of drawing ink — between the blades
of the pen near the point, and the ink will readily
flow from the point of the quill to the space between
the nibs of the pen. Do not have more than iV of
ink in the pen, for a larger amount will cause a pres
sure at the point with a tendency to blot. Never
hold the pen or quill over the paper, when filling the
pen. Before attempting to make a line, see that no
ink is on the outside of the blades of the pen. If
there is, clean it off with the penwiper. If none is
furnished with the bottle of ink, a soft cotton cloth
may be used. Always try the pen outside of the
cutoff line before starting to ink a drawing, not only
to see if the pen is working properly, but also to ad
just for the proper width of line. If interrupted
USE OF INSTRUMENTS 17
while inking a drawing, always see that the pen is
adjusted to the proper size of Hne, before taking up
the work again. When it becomes necessary to re
fill the pen, the sediment remaining between the nibs
should be wiped out by passing the penwiper be
tween the blades. This means that the pen should
be cleaned each time it is filled.
Using the drawingpen — Hold the pen with the
thumbscrew away from the body, with the end of
the index finger of the right hand bearing against
the outside blade just above the
thumbscrew. Incline the pen
slightly with the ruhng edge and
also in the direction of motion.
The proper relation of pen and
ruling edge is shown in Fig. 9.
The distance between the pen point
and the ruling edge should not be /vy. 3
too great lest the outer nib of the
pen be raised from the paper and make a ragged,
uneven line.
Erasing mistakes — If a mistake or blot makes it
necessary to remove some of the inked work, first
be sure that the ink is perfectly dry. Do not try
to erase with a few hard strokes, for time and patience
are necessary essentials to remove lines without
showing the effect of the erasure.
PLATE 1
Follow the directions given on the next pages.
Work carefully, accurately, and neatly. Keep the
pencil sharp, using the conical point for locating
points and the chisel point for drawing lines. Use
a light, fine line.
INKING
When inking, follow this order :
1. Horizontal lines. Ink those at the top first.
2. Vertical hues. Ink those at the left first.
3. Obhque hnes. Ink in the most convenient
order.
4. Printing. Use the writing pen.
DIRECTIONS FOR MAKING PLATE 1
Locate a point Ire" below the upper margin
line. Through this point draw a horizontal line
connecting the left and righthand margin lines.
Locate points on this line Iri'' in from each
vertical margin line. Erase the porti*. n of the line
between these points and the margin lines. This
should leave a horizontal line lOF' long. Draw
two vertical lines extending down from the ends of
this horizontal line a distance of li'\ Locate
points Te" apart on the lefthand vertical line.
Through the first point below the horizontal line,
draw a dotted horizontal line to the vertical line
at the right of the figure. Through the next point
below, draw a full horizontal line. Through the
next point below, draw a dotted line, and through
the lowest point draw a full line, completing the
figure. When drawing the dotted lines, make the
dashes of equal length and have them equally spaced.
Dashes should be not more than §'^ nor less than
A'' long, and the space between dashes should
equal about i the length of the dash.
Construct a square having sides 4'^ long, with the
left side 2" from the left margin line and the lower
side Ite" from the lower margin line. Using the
scale, divide the lower side. of the square into four
equal parts. Through these points draw vertical
20 MECHANICAL DRAWING
lines to the upper side of the square. From the
points where these vertical lines meet the upper side,
draw 45° lines to the left side of the square. From
the points on the lower side of the square, draw 45°
lines to the left side.
Construct a square having sides 4'^ long, with the
right side 2" from the right margin line and the
lower side liV from the lower margin line. Divide
the upper side of this square into four equal parts.
Draw vertical Unes across the square through the
points located. Through the points on the upper
side of the square draw 45° lines to the right side.
Through the points where the vertical lines touch
the lower side, draw 45° lines to the right side.
EXTRA PLATE
Draw a 71^^ square in the center of the sheet,
and copy one of the figures given on pages 22 and 23.
Note that the figures are determined by first draw
ing horizontal and vertical lines across the square
from points equally spaced on the sides.
INKING
The light lines of the figure are to be drawn
in pencil only; heavy lines are to be inked. When
inking, follow the order given for Plate 1.
22 MECHANICAL DRAWING
No 2
No. 4.
No 3 No. Q.
Plate 1, Extra Plate
USE OF INSTRUMENTS
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CHAPTER V
USE OF TRIANGLES
PLATE 2
On pages 26 and 27 are shown the different ways
in which triangles may be placed in relation to the
T square, both singly and in combination. From
the illustrations it will be seen that angles of 30°,
45°, and 60° with the horizontal or vertical may be
obtained by using triangles singly, while for angles
of 15° and 75° a combination of triangles is necessary.
When two points are so located that the line con
necting the two cannot be drawn with the triangles
in any of the positions shown on pages 26 and 27,
the quickest and best method is to place the pencil
on one of the points with one edge of a triangle
against the pencil, then, rotating the triangle until
the same edge coincides with the other point, draw
the line.
PARALLELS AND PERPENDICULARS
For drawing a parallel to a given line through a
given point, using the triangles, place one edge of a
triangle on the line with the second triangle bearing
against one of the other edges of the first triangle.
Holding the second triangle firmly, slide the first
USE OF TRIANGLES 25
one along its edge until it is in the required position.
In Fig. 10 is illustrated the method whereby a line
may be drawn through C parallel to M N. The
long edge of the 45° triangle is made to coincide with
the given line M N, and the long edge of the 60°
triangle is placed against one of the short edges of
the 45° triangle. These positions are shown in full
lines. From this position the 45° triangle is moved
along the edge of the 60° triangle until its long edge
coincides with the point C, or to the position shown in
dotted lines. The triangle is then in position to
draw the line X Y, which will be parallel to M N.
To draw a perpendicular to a given line through a
given point on or outside of the line, place the tri
angles in the same position as for parallels and then,
rotating the 45° triangle to the position shown in
dotted lines in Fig. 11, the required perpendicular
may be drawn. In Fig. 11, the line M N is the given
line, and X Y the perpendicular through either C or C.
Another method which may be employed for draw
ing the perpendicular is illustrated in Fig. 12. In
this case the short edge of the triangle is made to co
incide with the given Une and is then pushed along
the edge of the second triangle, thereby bringing the
other short edge to the point through which the re
quired perpendicular is to be drawn. In Fig. 12,
the line M N is the given line and X Y is the required
perpendicular through C.
In Figs. 10, 11, and 12 the 45° triangle was used as
the first triangle, although the 60° triangle might
have been used with the same result. Thus in Fig. 13
26
MECHANICAL DRAWING
USE OF TRIANGLES
27
28
MECHANICAL DRAWING
f^ia 1^
we have the same proposition as in Fig. 11, with an
interchange of triangles. Do not under any consid
eration place one edge of the right angle of a tri
angle against a line and use the other edge bounding
the right angle to draw a perpendicular to that line.
Good, accurate work cannot be done in this way.
PLATE 2
Make drawings of the geometrical figures given
in one of the rectangles shown on page 30. The
rectangle shown in the copy represents the margin
lines.
Keep the pencil sharp, using the conical point for
locating points and the chisel point for drawing lines.
Make very light, fine lines. Do not put the dimen
sions on the drawing.
INKING
Ink only the heavy lines shown in the copy.
Have the drawing complete in pencil before inking.
When inking, follow the order given on page 18.
30
MECHANICAL DRAWING
Plate 2
CHAPTER VI
WORKING DRAWINGS
PLATES 3 AND 4
If we look at an object through a transparent plane
and trace the outline as seen upon that plane, the
result is a perspective drawing of the object. The
relation of the object to the plane determines the
character of the drawing, and as the observer changes
his position relative to the plane his view of the ob
ject will also change, giving for different positions
entirely different drawings.
In perspective drawing all the points of sight pro
ducing the outline on the picture plane converge
to one point, namely the eye of the observer. This
causes all lines of the object in contact with the pic
ture plane to be in their true length in the drawing,
while all lines back of the picture plane will be short
ened. This foreshortening of lines with the in
ability to measure them, makes the perspective
drawing of very little value to the workman.
In making the working drawing or mechanical
drawing, we consider that all lines of sight producing
the picture are parallel to each other, thus giving
views of lines parallel to the picture plane in their
true length. In Figs. 14 and 15, page 32, are il
32 MECHANICAL DRAWING
Fig J 4
WORKING DRAWINGS 33
lustrated the two principles by which the perspective
drawing and the working drawing views are ob
tained. Note that in Fig. 14 none of the hnes are
seen on the picture plane in their true length, being
foreshortened because of the converging lines of
sight, while in Fig. 15 all the lines of one face of the
object are seen not only in their true length but also
in the true relation to each other.
The perspective drawing gives the general outline
and relation of parts in one view, while in mechanical
drawing more than one view is required to clearly
illustrate an object. Sometimes two views only
are necessary to show the shape or construction,
while in other cases three, and occasionally more,
are required. These two or more views, drawn ac
cording to given principles and in the proper relation
to each other, with enough dimensions for making
the object represented, constitute a mechanical
drawing.
THE THREE VIEWS
A freehand perspective drawing of a model from
which it is required to make the working drawing,
is given in Fig. 16, page 34. Let us, for convenience,
call the surface A the front surface of the object,
B the top surface, and C the side surface. To get
a view of surface A, we would look in the direction
indicated by arrows D, shown in Fig. 17. This view,
being of the front of the object, may be called the
front view, and may be placed at A, Fig. 18. The
view of the top surface, or top view, would be ob
34
MECHANICAL DRAWING
WORKING DRAWINGS 35
tained by looking in the direction indicated by the
arrows E. This being the top view, we would most
naturally place it above the front view, when group
ing the views. In Fig. 18, the top view is shown at
B, directly above the front view. To obtain the
view of the side of the object, or surface C, we would
look in the direction indicated by the arrows F, and
would get the view shown at C, Fig. 18. This be
ing the right side view of the object, it is placed at
the right of the front view. The relation of the three
views then will be as follows:
The top view is directly over the front view.
The side view is directly to the right of the front view.
A study of the three views given in Fig. 18 shows
that the height of the front and side views is the
same, the breadth of the front and top views is equal,
and that the height of the top view and breadth of
the side view are identical. From these statements
we may formulate the following rules:
1. The vertical dimensions on front and side views
are equal.
2. The horizontal dimensions on front and top views
are equal.
3. The vertical dimension on the top view equals the
horizontal dimension on the side view.
. It is not necessary to use the front face of the ob
ject as the front view. Any surface may be employed
as the front view, provided the other views are drawn
in the proper relation to this view\ Thus, in Fig. 19,
the surface C, drawn with its long edge in a horizon
tal position, is used as the front view, with surfaces
36 MECHANICAL DRAWING
A and B as top and side views, respectively. Still
another combination is shown in Fig. 20, page 37,
in which B is the front view, C the side view, and the
surface across the object from A, which may be called
A', the top view. In Fig. 21, the front view C in
Fig. 19 is drawn with its short edge horizontal. This
causes B to become the top view and A the side view.
Fig. 22 is the same as Fig. 20, with the top view
omitted. Notice that these two views show the shape
and size of the object as well as do the three views
of Fig. 20. This saves the drawing of the third view;
but in our practice, for the present, we will draw the
three views even though they may not be absolutely
necessary.
The block shown in Fig. 23, page 38 is the sartie
as that illustrated in Fig. 16, but with a mortise
cut into the block on the surface A. Three views
of this object are given in Fig. 24, in which the sur
face A becomes the front view, B the top view, and
C the side view. The mortise is represented on the
front view by the inner rectangle, and is expressed
on the top and side views by dotted lines. Inas
much as the mortise is not visible from the top or
side, some characteristic must be employed to dis
tinguish the visible from the invisible edge. Full
lines are employed to represent visible edges of the
object, and dotted lines for the invisible edges. These
lines may be grouped under one head and called
the main or primary lines of the drawing.
WORKING DRAWINGS 37
A'
B
C
F
■is 2
B
C
A
/
^j
7.2/
'
n
■g.22
38
MECHANICAL DRAWING
WORKING DRAWINGS 39
DIMENSIONS
The drawings we have just considered, while well
representing the objects, do not give enough in
formation for making the models. Not only must
the general outline, shape, etc., be shown, but the
dimensions necessary for making the model to a
definite size must also be given. In Fig. 25 is shown
the complete drawing of the model illustrated in
Fig. 24, not only the shape but the sizes as well be
ing given. To indicate these dimensions, other
lines and characters are employed which may be
grouped under one head and called the secondary
lines of the drawing. The names of the lines included
in this secondary group are witness or extension lines,
and dimension lines. Other characters used are
arrowheads. The figures placed on the drawing
are called dimensions.
A dimension line is one upon which the dimen
sion is placed and in which a break is made for the
dimension. iVrrowheads are placed at the extremities
of this line. A witness or extension line is one extend
ing out from the object line to and a little beyond
the dimension line, employed when the dimension
is placed outside the view. Different characters
of lines are used in different drafting rooms for these
secondary lines, so a system employed in one text
book could not conform to every draftingroom
system. For the work in this course, dotted lines
will be used for witness lines, and a full line, with
space reserved for the dimension, will be employed
40 MECHANICAL DRAWING
for the dimension line. The arrowhead should not
fall short of or project over the witness or object
line to which it goes, and should be made shorty
narrow, and pointed.
SUGGESTIONS FOR DIMENSIONING
Place all dimensions possible on one view, but
give dimensions to full lines in preference to dotted.
Avoid crossing horizontal and vertical dimension
lines.
So place the dimension that it can be erased with
out erasing a hne of the drawing.
Have horizontal dimensions read from the bottom
and vertical dimensions from the right of the draw
ing. See Fig. 25.
Do not use an oblique line as the vinculum of a
fraction; make this line par
I i I I ! } allel to the dimension line.
ia 1^ I J / hi Make F^ not 1/8''. Use great
' ^^ I 11 I I ^ care in making the figures ;
I I 1 ! 1 1 these are vital parts of the
^^ ^^ drawing.
Be sure to have the three di
mensions — length, breadth, and thickness— for the
main piece, also for all projections and recesses.
When it is impossible, because of the narrow
ness of the space, to get both dimensions and arrow
heads between the witness lines, the arrowheads,
or the dimension, or both, may be placed outside.
These three methods are shown in Fig. 26.
WORKING DRAWINGS
41
Do not use the " marks, when all dimensions are
in inches.
LOCATING THE DRAWING IN THE RECTANGLE
Unless a drawing is located in the center of the
rectangle in which it is drawn, the appearance of the
drawing is marred. It is, therefore, advisable to place
the views with reasonable spaces between, and with
equal margins at the top and bottom, also at the
right and left. The drawing shown in Fig. 27, surely
is more pleasing to the eye and makes a better im
pression than the one shown in Fig. 28. This is
due entirely to the proper placing of the drawing
within the rectangle bounding it.
The exact location of the drawing on the sheet
should be determined before a line is drawn. This
may be obtained by finding the full height and width
of the drawing, including the space between views,
42
MECHANICAL DRAWING
subtracting these dimensions from the height and
width of the sheet, and dividing the difference by
two. This will give the spaces at the top and bot
tom and the spaces at the right and left. Thus, in
\
^
\
^
\
+
^^
i
— 2 *
— B —
c^
3'^
^i(\i
^
/i
t
\ . .
1
Fig. 29
Fig. 29, the spaces A and A' may be obtained by
adding the height of the front view, ?>\" , the height
WORKING DRAWINGS
43
of the top view, 2" ^ and the space to be allowed
between the front and the top views, \" ^ and sub
tracting the sum,6i'', from the height of the rectan
gle, 9^', leaving the amount to be divided equally be
tween A and A^ 2h" . If we
make A and A' equal, then
each would be li^^ The
spaces B and B' may be ob
tained in the same manner by
adding the width of the front
view, 5i'', the width of the
side view, 2" ^ and the space
between views, \^\ making a
total of ^\" , Subtracting this
total from the width of the
rectangle, VI" , and dividing by
two, we have, VI" "^h" = Z\" ,
and Z\"2 = V^'. Therefore
nj,30
spaces B and B' should each be made H" . It will be
noticed in the above illustration that more space was
allowed between the front and side views than be
tween the front and top views. It is not necessary
that these spaces be equal; in fact it is better under
certain conditions that they be unequal. In the
figure we have been discussing, there is more blank
space horizontally than vertically; therefore there
should be more space between views horizontally
than vertically.
Let us consider one other condition. The drawing
shown in Fig. 30 is to be placed in a rectangle 9''
high and \2" broad. If we should allow V be
44 MECHANICAL DRAWING
tween the front and side views, the total horizontal
width of the drawing would be 5f\ This sub
T/y. 3/
tracted from the horizontal dimension of the sheet
would give 61^' to be divided into two equal parts,
for the spaces at right and left. These spaces would
then be SV each. Allowing V between the front
and top views, the total height of the drawing would
be 8y\ The difference between this height and the
height of the rectangle would be i'\ which, divided
by two, would give }'' each for spaces at the top
and the bottom of the drawing. A drawing placed
according to these conditions is shown in Fig. 31.
One can readily see that there is too much space
between the top and front views, when we compare
it with the spaces at the top and the bottom of the
drawing. If we reduce this space from V to ¥', we
will then have an additional i'' to be divided
equally and added to the spaces at the top and the
bottom, making each of these i'', instead of j' as
WORKING DRAWINGS
45
in the previous case. A drawing made to suit these
changed dimensions is shown in Fig. 32. Even
//> 32
though this is an improvement over the other con
dition, it still looks awkward with so much space
horizontally and so Httle vertically. The reason
for this is that we have been attempting to place the
46 MECHANICAL DRAWING
long dimension of the drawing in the short dimension
of the rectangle. By a rearrangement of views as
shown in Fig. 33, thereby placing the long dimension
of the drawing parallel to the long dimension of the
rectangle, a much more satisfactory result is secured.
It will, then, in all drawings, be necessary to find
which is to be the longest dimension, and place this
the long way of the sheet.
INKING THE WORKING DRAWING
It is well to divide the lines of a drawing into
groups before starting the inking, that systematic
and time saving work may be done. The primary
lines of the drawing — object lines — may be placed
in one group, the secondary lines in another group,
and the freehand work, which would include di
mensions, arrowheads, and printing, in a third group.
To distinguish the primary from the secondary lines,
different colored inks are often employed. Blacky
is always used for object lines, and red is often em
ployed for wdtness and dimension lines. Many times
the black is used for both. In the latter case the
distinguishing element is the character and size of
the line.
When inking drawings similar to those we have
been studying, observe the following order:
WORKING DRAWINGS 47
ORDER FOR INKING
Group 1. Object lines; heavy lines, with black ink.
Horizontal lines; the upper ones first.
Vertical lines; those at the left first.
Oblique lines; the most convenient way.
Group 2. Witness and dimension lines; light lines,
with red ink.
Horizontal lines; the upper ones first.
Vertical lines; those at the left first.
Oblique lines ; the most convenient way.
Group 3. Arrowheads, dimensions and printing;
with black ink.
Freehand, with writing pen. Work
from the upper left hand corner to
the lower right.
Group 4. Margin lines; heavy lines, with black ink.
When these are made the same size as
the object lines, they should be inked
with Group 1.
PLATE 3
After laying off the margin and cutoff lines, divide
the sheet into two equal rectangles by a vertical line
through the center. Two problems are to be solved
on this sheet, one at the left of the vertical line, and
one at the right, to be taken, respectively, from the
figures shown on pages 49 and 50. The problems
will be selected by the instructor.
Make three views, complete with dimension lines
and dimensions. If possible, leave at least 1'' be
tween the views, and locate the drawing in the rec
tangle with equal spaces at the right and the left, also
at the top and the bottom. Use Ught pencil lines.
INKING
Have the drawing complete in pencil before inking.
When inking, follow the order given on page 47.
WORKING DRAWINGS
49
Plates
50
MECHANICAL DRAWING
Plate 3
EXTRA PLATE
Divide the rectangle made by the margin Hnes
into two equal parts by a vertical line through the
center. The problem to be drawn in the rectangle
at the left will be selected from the upper part of
page 52, that for the righthand rectangle from the
lower part of the same page.
Make three views, complete with dimension lines
and dimensions. If possible, leave at least 1'' be
tween the views and locate the drawing in the rec
tangle with equal spaces at the right and the left, also
at the top and the bottom. Use light pencil lines.
INKING
Have the drawing complete in pencil before
inking. When inking, follow the order given on
page 47.
52
MECHANICAL DRAWING
Plate 3. Extra Plate
CHAPTER VII
OBJECTS WITH OBLIQUE SURFACES
PLATES 4, 5, AND 6
In rectilinear objects, such as we have presented
in Plate 3, the parallel lines of sight producing the
views are at right angles to the surfaces drawn,
thereby giving views which are exact reproductions
of the surfaces them
selves. In Fig. 34, is ^
shown a wedged piece
in which the front view,
in case we selected the
surface H, would be a
triangle with base M N
and altitude N S. The
side view would be a rectangle with the horizontal di
mension equal to S 0, and the vertical dimension
equal to N S, which is, of course, the same as the ver
tical dimension of the front view. The top view would
have for its horizontal dimension the distance M N,
the same as the horizontal dimension of the front
view. (See Rule 2, page 35.) For the vertical di
mension of the top view we must use the distance
S 0, which is the same as the horizontal dimension
^"'9. O^
54
MECHANICAL DRAWING
of the side view. (See Rule 3, page 35.) These
three views are shown in Fig. 35.
The top view does not show the exact size of the
o
s
s
S O
^^^
ft
1
g. 35
N
obhque surface of the wedge, that surface being fore
shortened due to the fact that the hues of sight pro
ducing this view are not at right angles to the surface.
It is not possible, with the three views shown, to give
the true shape of the oblique surface; but, knowing
that it is a rectangle, we may get one side by taking
the line S N, and the other side by using the lines S O.
TRACING
The original mechanical drawing made in the
drafting room very seldom finds its way into the shop,
the shop drawing being in the form of a blueprint.
OBJECTS WITH OBLIQUE SURFACES 55
The requirements of the blueprinting process demand
that the drawing be made on some transparent
material. The common practice is to make the
original drawing upon heavy drawing paper, and then,
usually before inking this drawing, make a tracing
upon some thin, transparent material, either tracing
paper or tracingcloth. From this tracing the blue
print may be made. The tracing is made in ink,
following the lines beneath, and the order of pro
cedure is the same as employed when inking the
original drawing.
PLATE 4
After laying off margin and cutoff lines, divide
the sheet into two equal rectangles by a vertical line
through the center. Two problems are to be solved
on this sheet, one at the left of the vertical line and
one at the right, to be taken, respectively, from
figures shown on pages 57 and 58. The problems will
be selected by the instructor.
Make three views, complete with dimension lines
and dimensions. If possible, leave at least \" be
tween the views, and locate the drawing in the rec
tangle with equal spaces at the right and the left, also
at the top and the bottom. Use light pencil lines,
INKING
Have the drawing complete in pencil before inking.
When inking, follow the order given on page 47.
I
OBJECTS WITH OBLIQUE SURFACES 57
Plate 4
58
MECHANICAL DRAWING
Plate 4
EXTRA PLATE
Divide the rectangle made by the margin Hnes
into two equal parts by a vertical line through the
centei. The problem to be drawn in the rectangle
at the left will be selected from the upper part of
page 60, that for the righthand rectangle from the
lower part of the same page.
Make three views, complete with dimension lines
and dimensions. If possible, leave at least 1'' be
tween the views and locate the drawing in the rec
tangle with equal spaces at the right and the left,
also at the top and the bottom. Use light pencil
lines.
INKING
Have the drawing complete in pencil before inking.
When inking, follow the order given on page 47.
60
MECHANICAL DRAWING
F/p. ^
^^ —
!
1
^'r
4:
•o
_,■
Eig /5
Plate 4. Extra Plate
PLATE 5*
Make three views — top, front, and right side — of
one of the pieces shown in perspective on pages 62
to 64. The problem will occupy the entire sheet.
Leave from V to W between the views, and locate
the drawing on the sheet with equal spaces at the
right and the left, also at the top and the bottom.
INKING
Have the drawing complete in pencil before inking.
When inking, follow the order given on page 47.
*NoTE. Plate 6 is to be finished before Plate 5 is taken from the
board.
62
MECHANICAL DRAWING
Plate 5
OBJECTS WITH OBLIQUE SURFACES
63
64
MECHANICAL DRAWING
Plate 5
PLATE 6
Make a tracing from Plate 5. When inking,
follow the order for inking given on page 47, except
the directions for the witness and dimension lines.
On the tracing make the lines included in Group 2
black and very fine. This will require that the
primary and secondary lines be inked in separate
groups, as when the colored ink is used; for the
former will be heavy lines and the latter fine lines.
As the width of the line is the only distinguishing
characteristic, it will be necessary to have the differ
ence in width quite marked.
i
CHAPTER VIII
ASSEMBLY DRAWINGS
PLATE 7
All of the drawings which we have made up to the
present time have been of a single piece and are
called detail drawings. When two or more pieces,
made to fit together, are drawn as they would be
when they are put together, we have an assembly
or construction drawing. The principles involved
in working out the views are the same as for the single
piece, although more care is
required in the selection of
views, in order to show the
construction clearly and at
the same time to use as few
dotted lines as possible.
Dotted lines on a drawing
are always confusing, and in
many cases one combination
of views will mean fewer
dotted lines than another.
A little time arid study will
determine the best combina
tion.
In Fig. 36 are shown two parts of a joint used in
woodworking, in which the tenon. A, of one piece
^:ilJ
/vy. 36
ASSEMBLY DRAWINGS
67
fits into the recess cut into the other piece at B. An
assembly drawing of this same joint, using three
views, is shown in Fig. 37. In reahty, two views will
show the details of construction clearly. These two
rn
7 ^7
views, with the dimensions for making each part,
are illustrated in Fig. 38. When dimensioning a
drawing of this character, dimension each of the com
ponent parts independent of the other. In Fig. 38,
the dimensions A, B, C, D, and E are complete for
making the horizontal piece and should be put on
before any attempt is made to dimension the vertical
68
MECHANICAL DRAWING
— X
1
>.
f
o
f
_^_j —
r
^
J
h B — 
r/g. 3 8
piece. When placing the dimensions on the vertical
piece^ it will be found that some of the dimensions
used for the horizontal piece may also be used for
the vertical. Thus the dimension D will serve not
only as the width of the cut on the horizontal piece,
but also for the tongue on the vertical piece ; and the
dimension B will serve equally well for the width of
either piece. This leaves simply the dimensions X
and Y to be added, in order to complete the dimen
sioning of the vertical piece, although the full di
mensions would include X, Y, B, D, and E.
PLATE 7
Divide the rectangle made by the margin hnes
into two rectangles by a vertical line through the
center. In the rectangles on pages 70 to 73 are
shown perspective drawings of parts of different
woodworking joints. Make three views — top, front,
and right side — of two of these problems. When
making the drawings, show the constructions clearly,
and choose the views showing the fewest dotted lines.
Leave about V^ between the views, and locate the
drawing in the center of the rectangle.
INKING
Have the drawing complete in pencil before inking.
When inking, follow the order given on page 47.
70
MECHANICAL DRAWING
H/2^
Mitre Joint
— End Mortise
anct 7e/7orf yJo/nf.
Plate 7
ASSEMBLY DRAWINGS
71
"5lflO
Blind Mor//3e a/7c/
Tenon Jo/nf.
■ ll^
^
Ho/e exfencfs
/n^o p/ece /p inc/7es
■Enc/ Lap Jo/nf
Plate 7
72
MECHANICAL DRAWING
"pr^rra
^K4J
Box Jo/nf. — '2
•f^
 Door Joint '^N^Vt^^l
,i A
K£
Drainer Jo/nt
Jr^^
■Doi/'efa// La JO <Jo/n/.
Plate 7
ASSEMBLY DRAWINGS
73
Th/s £ide of /70/e fa /3Gr^
i'li^^ ' . ^o /// f a/per ec/ 
3/c/g of p/n _s4::d='T*
Pin Joint.
Tab/e Leg Jo/rrf.
■Ooyefo// Mor//se sJoZ/yf.
Dove fa// Drat^er Joint —
vn
Nco
ity*
^
I
,¥
\
1
5
16
■ 1
[_2ii
Plate 7
EXTRA PLATE
On pages 75 and 76 are given detail drawings of
parts of woodworking models. Make assembly
drawing, showing the construction in full lines, if
possible. One problem will occupy an entire sheet.
INKING
Have the drawing complete in pencil before inking.
When inking, follow the order given on page 47.
ASSEMBLY DRAWINGS
75
:::::c
~T^T
1
i^ ^^i?
f^i
TsT
1
1
/i
^ bi'
r/i
Jcal
1"
Defer //s of
Haiync/?ec/ Mor//se a/7c/ 7^/7or7 o/fc*//?/
r:ni
oj
J
— 2
i(\j
^^
Oefai/s of Brcfce Jo/nt
Plate 7. Extra Plate
76
MECHANICAL DRAWING
^ i
r "^4
t
CM
'
f
'
^
1
— Two pieces //Ae fh/s
.—
^CQ
r
!
p^
roico
— ^ C/?^ pJece //Ae //b/Is —
_
 Th/o p/eces //ke //7/s. —

TTvo /D/'eces //Ae //?/3
1^
7'^
TTvo p/'eces //Ae //7/\s.
Orpe p/'ece //Ae //?/3.
De/a//^s of
/?ec/ar7pc//c// Sox. —
Plate 7. Extra Plate
EXTRA PLATE
On pages 78 and 79 are given the assembly draw
ings of some woodworking joints. Make the detail
drawings.
INKING
Have the drawing complete in pencil before inking.
When inking, follow the order given on page 47.
78
MECHANICAL DRAWING
—
'i
—
^
■t
•1
1
/
t
1
1
■ — 2 ■
CVI
Brc7cec/ Mor/^/se and 7e/^or7 xJo/'nf
^*
\
\*
^'
bZ ^/
— ^
■/«
t
"X
•■/
"!!*
I
^M II 1
to
S 1
./^«
Scar^ ^o/r>/.
Plate 7. Extra Plate
ASSEMBLY DRAWINGS
79
lrtl ^
»T ,1
7^ *'
MAA
i
^
?
^2
Dov
eA3
//_
Jo/n/:
a
7
^8^
&
2 —
zr ,
(0 .
1
1
fVJ

Ha/f Dove /a// Lop <Jo/nt.
Plate 7. Extra Plate
CHAPTER IX
USE OF INSTRUMENTS
(Curved Work)
PLATE 8
The compasses — As before stated, the compasses
are provided with pencil and pen attachments and a
lengthening bar. The lengthening bar is inserted
between the fixed leg of the instrument and either
the pencil or pen attachment, when it is desired to
draw an arc whose radius is greater than the capacity
of the regular instrument. For circles of large
radii, the knuckle joints in the legs of the instrument
should be bent to bring both needle point and pencil
or pen attachment at right angles to the paper.
This is absolutely necessary when the pen attach
ment is used, in order that both nibs of the pen come
in contact with the paper.
The compasses should never be placed on the scale
when setting for a radius; this will eventually make
holes in the scale, thereby ruining its accuracy.
Measure to the left from the center about which the
circle is to be drawn a distance equal to the radius
of the circle, and after locating the needle point ex
actly at the center set the pencil point to the mark
through which the arc is to be drawn. Use only
one hand when drawing a circle, grasping the in
strument by the handle where the two legs are jointed.
Rotate the compasses from the left, up over the top,
USE OF INSTRUMENTS 81
down through the right and bottom to the starting
point. Always rotate the compasses in this direction,
beginning at the left. Go over the Une only once,
making a hght, fine fine. An attempt to make a
heavy line will probably result in spreading the legs
of the instrument, thus increasing the radius.
The dividers — While the dividers are used for
transferring distances from one part of the drawing
to another part, they should never be employed for
transferring a measurement from the scale to the
drawing. Measurements on the drawing should be
made directly from the scale. The dividers are most
useful for dividing a line into a given number of
equal parts, when the scale cannot be employed for
the purpose. When thus used they should be held
by the handle at the top of the instrument and should
be rotated first on one side of the line and then on
the other. Should the first setting not divide the
line equally, a second setting, and probably more,
will be required. If the divider is provided mth a
hairspring adjustment, this will be found very use
ful for adding to or subtracting from the original
setting. Do not push the points of the instrument
through the paper until the exact setting has been
obtained.
The bow instruments — These instruments are used
on small work for the same purposes as the large ones
are employed for large work, the directions for their
use being the same as those given for the large com
passes and dividers. The bow instruments should
be employed for everything within their capacity.
/5o/3(^
PLATE 8
Follow the directions given on the following pages.
Use extreme care when working out the figures.
Follow the directions for the use of the compasses
and dividers.
INKING
The margin lines are the only straight lines to be
inked. These should be inked last. All the arcs,
with the exception of the circle about the point B,
are to be inked. When inking the arcs, begin with
the largest.
DIRECTIONS FOR MAKING PLATE 8
Three inches below the upper margin hne, draw a
light horizontal line connecting the left and right
hand margins. On this line and 2i'' from the left
hand margin, locate a point. Letter this poinc A.
Locate a point, to be lettered B, 4i'' to the right
of point A; and 4i'' to the right of B locate a point,
which we will call X. Through the points A, B,
and X draw vertical lines about b'^ long, extending
equidistant above and below the horizontal line.
Draw a horizontal line 2Y' above the lower mar
gin line, connecting the left and right hand margin
lines. On this horizontal line and 2'' to the left of
the right hand margin line, locate a point. This
point we will call D. Beginning with point D and
measuring to the left, locate four more points 2\"
apart. Call these points E, F, G, and H. Through
these points draw vertical lines about V long, pro
jecting equally above and below the horizontal line.
With point A, on the upper horizontal line, as a
center, draw a circle having a ^" diameter. Using
the same center, draw a dotted circle of IV' radius.
When drawing the dotted line, make the dashes of
equal length and have them equally spaced. Dashes
should not be more than \" long and the space
between dashes should equal about \ the length
84 MECHANICAL DRAWING
of the dash. Again using the center A, draw a circle
of 1'' radius. This circle is to be drawn a full line.
Concentric with the three circles just drawn, make a
dotted circle of 1'' diameter.
With a 1'' radius, draw^ a circle about the point B.
Using the 45° triangle, draw lines through the center
of this circle, dividing the circumference into eight
equal parts. Beginning at the point where the verti
cal line through the center cuts the upper part of the
circle and passing around to the right, number these
points from 1 to 8, consecutively. With point 1
as a center, and with a radius equal to the distance
from 1 to B, draw a semicircle to the right of the
vertical line. Using point 2 as a center, with the
same radius, draw an arc from a point where it would
intersect the semicircle about point 1, to the right,
until it strikes point B. Draw about point 3, to
the right, with the same radius, an arc from the point
of its intersection with the arc about point 2, until
it reaches point B. Complete the figure, using,
in succession, points 4, 5, 6, 7, and 8. After the arc
about point 8 is drawn, it will be necessary to extend
the arc drawn about point 1 in order to make this
arc the same as the others.
With X as a center, draw a circle having a diameter
of 4''. Using the bow dividers, divide the horizontal
diameter into six equal parts. Beginning at the left,
at the point where the horizontal line cuts the arc,
letter the points a, b, c, d, e, f, and g. Point d will
coincide with X. With b as a center, and a radius
equal to the distance from b to a, draw a semicircle :
USE OF INSTRUMENTS 85
above the horizontal line. This semicircle should
touch the point c. With the same radius, draw a
semicircle below the horizontal line, using f as a
center. This semicircle should touch the points e
and g. With c as a center, and a radius equal to a c,
draw a semicircle above the horizontal line. This
semicircle should touch the point e. Using the same
radius, draw a semicircle below the horizontal line,
with the point e as a center. This semicircle will
touch g and c.
With points D, F, and H, on the lower horizontal
line as centers, with a radius of 1}^', draw semi
circles above the horizontal line. With E and G as
centers, and the same radius, draw semicircles below
the horizontal line. Again using points D, F, and
H as centers, draw semicircles with a U^ radius above
the horizontal line. Below the horizontal line draw
semicircles about points E and G, using a f radius.
k
k
EXTRA PLATE
Draw a Ih" square in the center of the sheet, and
work out one of the figures shown on page 87. The
centers for the arcs are determined by drawing hori
zontal and vertical lines across the square from points
equally spaced on the sides.
INKING
Only the heavy lines of the figures are to be inked.^
Ink the large arcs first.
USE OF INSTRUMENTS
87
No. a.
a\
S3
BD
M>
No. 4.
No. 5. No. &
Plate 7. Extra Plate
EXTRA PLATE
Draw one of the figures shown on page 89. All
the fines radiating from the centers C may be ob
tained by using the triangles on the T square, either
singly or in combination. Work carefully and
accurately. Do not put the dimensions on the
drawing.
INKING
Ink only the heavy lines of the figure. Ink all the
arcs first, and then the straight lines.
USE OF INSTRUMENTS
89
Plate 7. Extra Plate
CHAPTER X
CYLINDRICAL WORK
PLATES 9 AND 10
Whenever a circular piece or circular hole is shown
in a mechanical drawing, a line is used to indicate the
location of the center of the piece or hole. This line
is known as a center line, and is included in the group
of secondary lines already referred to. It represents
the axis of revolution of the piece and becomes the
axis of symmetry in the drawing. In Fig. 39 are
shown two views of a double lever. The main center
line of these views is the horizontal line marked
"primary center line." This is the center line of the.
main cylinder about which the model is constructed,
and also serves as a center line for the hole through
this main cylinder. As the cylinder and hole are
concentric, the one center line will answer for both.
On the circle view of a cylinder or a cylindrical
hole, two center lines, both passing through the center
of the circle, are drawn. These two lines are usually
at right angles to each other. Thus, in Fig. 39, the
vertical center line is drawn at right angles to the
other main center line. This vertical center line is
also a primary center line of the drawing, and, had
the top view been drawn, would have extended up
CYLINDRICAL WORK
91
■Secor?c/<7ry Cerrfer /./nes
L::r:
Rr/mary
Cer?fe/ //>7e
Fig. 39
92 MECHANICAL DRAWING
through that view, connecting it with the front view,
as the horizontal center Une connects the front and
side views.
The two small cylinders on the arms extending out
from the main cylinder also require center lines. As
these are not the main center lines about which the
drawing is made, they do not connect the two views,
although they have to be shown on both views.
These may be called secondary center lines. The
vertical center line serves not only as the main center
line for that view, but also as one of the center lines
of the small cylinders and the holes in these cylinders.
Alternate long and short dashes may be used to
distinguish the center line from the other secondary
lines of the drawing, although, as with all of these
lines, this characteristic is dependent upon the sys
tems used in the different drawingrooms in which the
drawings may be made. These lines should be inked
with the other secondary lines, and should be the
same width and color.
When a series of holes equidistant from a given point
are to be represented, a line, called a circular center
line, is employed. As its name implies, it is a circle
drawn about the point from which the holes are equi
distant, passing through the centers of the holes.
The line X, Fig. 40, is a circular center line answering
as one of the center lines of all the small holes repre
sented on the front view. The other center line for
these holes is a portion of a radial line drawn through
the center of the circle representing the hole. These
lines should not be drawn to the center of the piece,
CYLINDRICAL WORK
93
but should extend only through the circles for which
they are the center lines. This is shown clearly in
Fig. 40. Notice also on this figure the center lines for
the small holes on the side view.
The primary center lines should be the first pencil
lines to be drawn, and should be so located that when
the drawing is complete it will be in the center of the
rectangle. x\fter drawing the center hues, the meas
urements should be made from these and the drawing
built up about them.
The introduction of the curved hnes of the object
and the center lines necessitates a new order for
inking the drawing. When inking drawings similar
94 MECHANICAL DRAWING
to those shown in Figs. 39 and 40, follow the order
given below:
ORDER FOR INKING
Group 1. Object lines; heavy lines, with black ink.
Arcs; begin with the largest.
Horizontal lines; the upper ones first.
Vertical lines; those at the left first.
Oblique lines ; the most convenient way.
Group 2. Witness, center, and dimension lines;
light lines, with red ink.
Arcs; begin with the largest.
Horizontal lines; the upper ones first.
Vertical lines; those at the left first.
Oblique lines ; the most convenient way.
Group 3. Arrowheads, dimensions, and printing;
with black ink.
Free hand, with writing pen. Work
from the upper left to the lower right.
Group 4. Margin lines; heavy lines, with black ink.
When these are made the same size
as the object lines, they should be
inked with Group 1.
PLATE 9
Divide the rectangle made by the margin Hnes
into two equal rectangles by a vertical line through
the center. In the lefthand rectangle draw two
views of one of the objects shown in perspective on
page 96, and in the righthand rectangle draw two
views of one of the models shown on page 97.
Select the views having the fewest dotted lines,
consistent with a clear representation. Locate the
center lines to bring the drawing in the center of the
rectangle.
INKING
Have the drawing complete in pencil before inking.
When inking, follow the order given on page 94.
96
MECHANICAL DRAWING
Plate 9
CYLINDRICAL WORK
97
Plate 9
EXTRA PLATE
Make two views of one of the objects shown on
page 99.
Follow the general directions given for Plate 9.
CYLINDRICAL WORK
99
'4H
h/2i
Be// CrcrryA
Plate 9. Extra Plate
PLATE 10
Copy the two views shown in one of the rectangles
on pages 101 to 106, and work out the third view.
The problem will occupy the entire sheet. Locate the
center lines to bring the drawing in the center of the
sheet. Print the name of the piece under the draw
ing, making the capitals t&" high and the small
letters \" high.
INKING
When inking, follow the order given on page 94.
CYLINDRICAL WORK
101
1
 ~y
1 1
1 1
1
1
1
1
•
'^ — zh—
/'
%
— 2i
V
J
_[^
1
1
r
1
1
!
1
— i — \~/
— zi^
* 2i *
1
1 1
1 1
1
(
Plate 10
102
MECHANICAL DRAWING
Plate 10
CYLINDRICAL WORK
103
1 ■
1 • 1
f^h— !v
a
h//'^i— /iH
"i f f
^ ! '^
Connecf/np /^ocf Sfrc7 p. 
Plate 10
104
MECHANICAL DRAWING
Plate 10
CYLINDRICAL WORK
105
o^
■oioo
J
3
■ Eccer7/^n'c.
^ii
I'^A
, __v
4i
^3
RacA/'n^ G/oncf.
Plate 10
106
MECHANICAL DRAWING
1
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4,
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Plate 10
EXTRA PLATE
Copy the two views shown in one of the rectangles
on pages 108 and 109, and work out the third view.
The problem will occupy the entire sheet. Locate
the center lines to bring the drawing in the center
of the rectangle. Print the name of the piece below
the drawing, making the capitals ye" high and the
small letters V high.
INKING
When inking, follow the order given on page 94.
108
MECHANICAL DRAWING
::.r
\ '^A <
Tr/p/e Le\/er
Plate 10. Extra Plate
CYLINDRICAL WORK
109
K—
1
f
Base /s reef ar7
Qu/ar /n for/n.
1
1
TT
1
1
' 1
•0
1
1 '
1
1
\
i
Ik
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1
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1
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;
: .1,
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1
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^a
Ver
yy
Plate 10. Extra Plate
CHAPTER XI
SCALED DRAWINGS
PLATE 11
Many times the object to be represented in the
drawing is of such a size that it is impossible to draw
it full size upon a sheet that may be conveniently
handled in the shop. In cases of this kind, the draw
ing is made to a reduced scale, and is called a scaled
drawing. A scaled drawing is one in which the length
of all the lines of the drawing bears a definite ratio
to the length of the corresponding lines of the object.
Thus in a dramng made onehalf size, each Hne of
the drawing will be onehalf the length of the cor
responding hne of the object.
Our United States standard system of measure
ments requires that the denominator of the fraction
used in our scale shall be some multiple of two. The
draT\dngs, therefore, wdll have to be made , i, i or
i size. It will be readily seen that it would be
practically impossible to measure most dimensions, if
a twothirds or onesixth scale were employed.
Drawings should always be made to the largest pos
sible scale. If it is possible to use threefourths
size without crowding, do not make the drawing one
half size. It is, of course, easier for the workman to
\
SCALED DRAWINGS 111
work from the fullsized drawing, and the smaller
the scale the more difficulty there will be in reading.
Full size dimensions should be placed on the drawing;
not the measurements of the drawing, but the di
mensions to which the object is to be made.
A statement giving the scale to which the drawing
is made should be printed on each scaled drawing.
There are two ways in which this may be expressed.
The one commonly used on machine drawings is
Scale, I Size, or Scale, i Size. Because of the small
scales employed, the architect uses the following:
Scale, 3'' = r, or  in. = lfL
PLATE 11
Copy the two views given in one of the rectangles
on pages 113 to 116, and work out the third view.
Make the drawing to the largest possible scale.
Place the title and the scale to which the drawing is
made below the drawing.
INKING
When inking, follow the order given on page 94.
SCALED DRAWINGS
113
W\
^— 2 
1
1
^'.
2
i
.t
1 ,
i
i
\^
I'u
^ '
1
Angle P/afe
PacA/r ? g G/cfnc/.
Plate 11
114
MECHANICAL DRAWING
1
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1

1
.1
1
^ZZ^J
3
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— 2.^
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r
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r'"
A
■ P/vof Bear/na.
V
f 94
^1
34
V
€
'ii
33
Lf
_t_i
i Si
3^'l
Sv^ivel Bean' I
09^
±
Plate 11
SCALED DRAWINGS
115
Plate U
116
MECHANICAL DRAWING
Be// Cran/< Lever
7^
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Plate 11
EXTRA PLATE
Copy the two views given in one of the rectangles
on page 118, and work out the third view. Make
the drawing to the largest possible scale. Place the
title and the scale to which the drawing is made be
low the drawing.
INKING
When inking, follow the order given on page 94.
118
MECHANICAL DRAWING
£.cce/ifr/c C/a^n js/n o 3eor//7 ir.
iHrH
'iH
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3ecrr/>7Q for /^/ar?er Oenfer
Plate U. Extra Plate
CHAPTER XII
SECTIONAL VIEWS
PLATE 12
In the problems which have been presented thus
far in the course, emphasis has been placed upon ex
pression with full lines in preference to dotted ones.
Dotted lines are confusing on any
drawing, and should be avoided
wherever possible. To eliminate
the dotted lines caused by the
three views we have already dis
cussed, a system by which the in
terior of the object may be shown
in full lines is employed. Views
of this character are known as sec
tional views, and are obtained by
passing an imaginary cutting plane
through the object and making a
drawing of the portion of the ob
ject remaining after the part cut off by the cutting
plane has been removed.
A double flanged cylinder with a circular hole pass
ing through it is shown in Fig. 41. Let us imagine
that this cyhnder is cut in halves by a vertical plane
120
MECHANICAL DRAWING
■^9.
^^2
passing through the axis. After passing this cutting
plane through the piece, and removing the front half
of the cylinder, we would have what is represented
in Fig. 42. Two views of the model
shown in perspective in Fig. 41 are
given in Fig. 43, while in Fig. 44
are shown two views after the imag
inary cutting plane has been passed
through the piece. It will be seen
that the front view only is altered,
the top view remaining the same.
The model represented is a com
plete cylinder, and not a half cylin
der; therefore the complete top view
is necessary. The front view, which
really represents only onehalf of the
cylinder, is produced by the imaginary cutting plane,
and not an actual cutting plane; hence the complete
top view.
A comparison of the full front view in Fig. 43 and
the sectional front view in Fig. 44 brings out the fact
that the hole through the piece is represented by
dotted lines on the former and by full lines on the
latter. Also note that portions of the horizontal
lines representing the lower part of the upper flange
and the upper part of the lower flange have been
omitted on the sectional view. It is common prac
tice to omit the dotted lines, when the representation
is complete by full lines, even though every line of the
object is not shown on the drawing. Had the flanges
been square, as shown in Fig. 45, it would have been
SECTIONAL VIEWS
121
1
1
1
1
1
1
^^9
^3
/^f'g, *^*f
best to draw these dotted lines, in order to show the
corner on the front view.
The obhque hnes drawn across portions of the
sectional views are called section lines. These are
drawn only where the material of the model is cut
by the cutting plane. In Figs. 44 and 45, they are
not drawn across the area representing the hole
through the piece, but only across those portions of
the model where the cutting plane has come in con
122
MECHANICAL DRAWING
tact with the material of which the model is made.
The section Hne may be made at any angle and in
either direction. The most common angle is 45°,
and the direction is
usually from the lower
left to the upper right,
probably because of
its convenience. Sec
tion lines should not
be drawn with pencil,
nor should they be
spaced with the in
struments or scale.
They should be inked
with black ink, with a
line finer than the fin
est line of the draw
ing, and should be
spaced with the eye,
care being taken not
to have the lines too
close together. For
average work, spaces
should be about ^''.
When two or more
pieces are in contact
and a sectional view is used, the section lines for the ,
several pieces should be drawn in opposite directions.
Should these pieces be so placed that one of them
is in contact with two or more, it will be necessary
to change the angle of the lines as well as the direction.
SECTIONAL VIEWS
123
I
124 MECHANICAL DRAWING
In Fig. 46, page 123, the inner piece or spindle is in
contact not only with the bearing, but also with the
yoke at the end of the piece. The section lines for
the spindle are drawn at an angle of 30° with the
horizontal, from the upper left to the lower right.
For the bearing, the lines are drawn at an angle of
30° from the lower left to the upper right. The
lines for the yoke are at an angle of 45°, and, though
drawn in the same direction as the lines of the spindle,
the difference is shown by the change in angle.
The introduction of the section lines causes an
other group to be added to those already classified
for inking. In all of the work hereafter, use the order
for inking given below.
ORDER FOR INKING
Group 1. Object hues; heavy lines, with black ink.
Arcs; begin with the largest.
Horizontal lines; the upper ones first.
Vertical lines ; those at the left first.
Oblique lines; the most convenient way.
Group 2. Witness, center, and dimension lines; light
lines, with red ink.
Arcs ; begin with the largest.
Horizontal lines; the upper ones first.
Vertical lines; those at the left first.
Oblique lines; the most convenient way.
Group 3. Arrowheads, dimensions, and printing ; with
black ink.
Free hand, with writing pen. Work from
the upper left to the lower right.
SECTIONAL VIEWS 125
Group 4. Section lines; very light, black lines.
Finer than any other line of the drawing.
Group 5. Margin lines; heavy lines, with black ink.
When these are made the same size
as the object lines, they should be inked
with Group 1.
PLATE 12
Copy the two views shown in one of the rectangles
on pages 127 to 131. Make one of the views a sec
tional view.
INKING
When inking, follow the order given on page 124.
Use this order on all of your future work.
SECTIONAL VIEWS
127

1 1
«
/
1 1
'i
~?"rir
? ^

L.
^i
Piston
Plate 12
128
MECHANICAL DRAWING
F/anQecf Cou/o//'r p.
[H
i
i !
_ J..
T
r 00
If
P/sfon Soc /y.
Plate 12
SECTIONAL VIEWS
129
Plate 12
130
MECHANICAL DRAWING
Plate 12
SECTIONAL VIEWS
131
2k
w
ro«o[v<
00,50
:=^
37i
3 team En cf /ne Cy/mc/er Hecrc/. —
Guide for S^/ve/ Hecrcf
Plate 12
EXTRA PLATE
Copy the two views shown in one of the rectangles
on pages 133 and 134. Make one of the views a
sectional view.
INKING
When inking, follow the order given on page 124.
SECTIONAL VIEWS
133
Governor ^u//e y.
Plate 12. Extra Plate
134
MECHANICAL DRAWING
i
D/orr?e /ers ( y/ \^e/7 .
arc ot sc/ e^es /WaAe
of croi^r? ,f; mo/s fhcrr>
Cone Po//e y
,^£^
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F/anQ<?cf Pu/Ze y
Plate 12. Extra Plate
CHAPTER XIII
PARTIAL SECTIONS
PLATE 13
In order to show both the exterior and the interior
in full lines in a single view, a half section, shown in
Fig. 47, is often employed. This, it will be noted,
is a drawing of the model shown in perspective in Fip*.
41, and the front view is a combination of the front
views given in Figs. 43 and 44, page 121, the right
half being the same as the right part of the full view,
while the left portion is the same as the left half of the
sectional view. The cutting plane to produce this
front view would pass along the horizontal center line
of the top view to the center of the piece, then along
the vertical center line to the front of the view. De
noting the path by letters, the cutting plane would
pass along the line ABC. Thus it will be seen that
the path of the cutting plane need not be a straight
line, as was the case in Figs. 44 and 45. In Fig. 47 the
place where the cutting plane ends is shown by a full
object line, but it is often the practice to use simply
the center line to limit this sectioned area. This
method is shown in Fig. 48. In this view all of the
dotted lines are omitted.
Another instance of a cutting plane not being con
136
MECHANICAL DRAWING
i
1
P
>
i
i
m
1
1
F/s^. ^7
F/ff. ^G
tinuous is shown in Fig. 49. In this example the
cutting plane passes along the horizontal center line
to the shaft upon which the disc is mounted, thence
around the shaft to the horizontal center line again,
and along this center to the outside of the piece.
This leaves the spindle or shaft in full on the front
view, which leads to the statement that soM, cylin
drical parts should never he shown in section. The full
length of the shaft is not shown in the front view and
PARTIAL SECTIONS
137
138 MECHANICAL DRAWING
ends at top and bottom in what are termed broken
sections. This figure also shows the breaking of the
section fines for the dimension, when the dimension
has to be placed in the sectioned area. Note that
the breaking of the section lines brings into prom
inence the 5x6^' dimension on the front view.
Arms of pulleys and handwheels, ribs on castings,
etc., should be placed back of the cutting plane,
when a sectional view is used. The application of
this statement to the arms of a pulley is shown in
Fig. 50. The line of the cutting plane to produce
the sectional view would be along the vertical center
line of the side view. This would make the arm of
the pulley in section; but, in cases of this character,
we draw the sectional view as though the plane passes
through the rim and hub, leaving the arm as a full
view. By this method one is able to distinguish,
by a glance at the sectional view, the character of
the connection between the hub and rim of a pulley.
A pulley with a web connection between rim and hub
is illustrated in Fig. 51, and a comparison of the two
sectional views will show the way in which one may
differentiate between the two designs. Had the
sectional view of the arm pulley been made by passing
the cutting plane through the arm, the resultant
view would have been the same as the sectional view
of the webbed pulley, with no opportunity to dis
tinguish between the two, except by reference to
the other view. By placing the arm back of the plane
of the section, we emphasize the character of the de
sign.
PARTIAL SECTIONS
139
140
MECHANICAL DRAWING
^ig ^^
Fig. 53
The sectional view of the model shown in Fig. 52
gives the impression of a conical piece, while in reality
it is a cylindrical piece with supporting ribs and rec
tangular base. While it is possible to see the exact
shape by the combination of the front and top views,
yet no one view should give a wrong impression. If,
instead of the views given in Fig. 52, we had used
the views shown in Fig. 53, the sectional view would
give the correct impression of the general shape of
the object. This would, then, be the proper view
to employ. It is obtained by placing the ribs back
PARTIAL SECTIONS
141
of the plane of the section, as we did the arms of the
pulley in a previous illustration. This drawing also
shows the size of the fillet where the cylinder joins
the base, something which was not shown at all in
Fig. 52.
From the drawing given in Fig. 50, it is impossible
to tell the shape of the arm of the pulley. We can
Fig. 54
get the width and thickness, but whether it is rec
tangular, flat on the sides with rounded corners, or
elhptical in section, we do not know. The section
drawn on the arm at the right of the center shows the
fcross section to be an ellipse. Here the view is
^shown at right angles to the cutting plane, a practice
[quite common in cases of this character. Often the
142 MECHANICAL DRAWING
line of the cutting plane is given and the section drawn
in another place. This is illustrated in Fig. 54. In
this figure the lines A B and C D represent the lines
of two cutting planes, and the figures below the draw
ing show the shapes of the sections. It is necessary
to distinguish them by letters and notes, as shown in
the figure.
PLATE 13
Copy the drawing given in one of the rectangles
on pages 144 to 146, making the upper half of one of
the views in section.
144
MECHANICAL DRAWING
PARTIAL SECTIONS
145
#■ .
^SH
xd
Secf/onAB
'Tf\
\ .
)
1 A
\ 1
T.^
/
1
1 ri^
0
/
^

—
I'
Gear B/anA.
Fr/cf/on Cone.
Plate 13
140
MECHANICAL DRAWING
4__I
t
i:
r
— /i^
/°//o/ i/V/7ee/.
Plate 13
EXTRA PLATE
Follow the directions given in one of the rectangles
on pages 148 to 150.
148
MECHANICAL DRAWING
v5ec//o/7 cn
Make s/c/e i^/epv />? sec f /or?.
Eccenfr/c.
o 3ecf/o/7a/ i^/ew.
L.
t'i^
8i
C/7UCA.
Plate 13. Extra Plate
PARTIAL SECTIONS
149
K/gM^ cy sec f /on a/ y/e^/
% ^
l^
Z
r
^^
1
2i H
■ ■3 p'fyc//e Crar7A /^cgc/.
f« 2
_^ I I
Bronz0
P/a/r? Sear/'ng' i^//h Sush/n qr. 
Plate 13. Extra Plate
150
MECHANICAL DRAWING
Plate 13. Extra Plate
APPENDIX
CHAPTER XIV
LETTERING
CAPITALS
Good lettering is an essential to good work in
mechanical drawing. Plain, simple^ wellpropor
tioned, properly spaced lettering will improve the
appearance of any drawing, no matter how beauti
fully it may be executed otherwise; and it is equally
true that the appearance of the drawing will be ruined
by poor lettering.
On almost all mechanical drawings, the Gothic
type, an example of which is shown on page 154, is
employed. Sometimes all capitals are used, but in
the majority of cases the capitals and small letters
will be found. When all capitals are used, the capi
tahzed letters are made higher than the others.
(See Fig. 55.) A careful examination of the alphabet
will show that the letters are composed of either
straight lines, ellipses, or combinations of the two.
For instance, the capitals H, N, M and others are
composed entirely of straight lines ; the and Q are
elHpses; C and G are portions of ellipses; while
D, P, R, and others, are combinations of parts of
ellipses and straight lines. Combinations of a similar
nature will be found in the small letters.
154 MECHANICAL DRAWING
\BCDErQHIJKL
MNOPQRSTU
VWXYZ
abcdefghijklmno
pq rsfuvwxyz
1234567890
4i 2i 7
LETTERING 155
The main body of the small letter should be two
thirds the height of the capital. A good size for
practice work, in fact, for most lettering on a drawing,
is 1^ of an inch for capitals and i of an inch for the
main part of the small letter. Lines should always
be drawn regulating the height, and the letters should
exactly fill the space between the lines.
Particular care should be used to make the slant of
the letters uniform. This slant may be made any
thing between 60° and 75° with the horizontal, the
latter being the better angle. In .
the capitals A, V, X, and W, and \l/Af\JI j \^
the small letters v, x, and w, the '^'s^^
angle of the component parts may / / I'j H
be determined by the use of a center / njss^
line. In the word '^Vanity," Fig. 55,
the general slant is shown by the letters I, N, and T,
and the slope of the parts of the letters V, A, and Y
is obtained by laying off equal spaces each side of
center lines drawn parallel to the letter I.
The manner of obtaining the slant of the curved
letters may best be illustrated by using O as an ex
ample. Draw a parallelogram (see Fig. 56) in
which the upper and lower lines shall limit the height
of the letters, and the right and lefthand lines shall
represent the slant. Divide each side into two equal
parts. This gives the tangent points of an elhpse
to be drawn within the parallelogram.
It should be perfectly understood that all of this
work, with the exception of the lines to regulate the
height of the letter, should be executed free hand,
156 MECHANICAL DRAWING
and that as soon as the student can trust himself,
all of the construction for the curved letters should
be omitted. When inking, only a small amount of
ink should be used on the pen, and great care should
be exercised not to spread the points. Avoid all
shading and shade line effects.
No definite rule can be given for the space between
letters, this space varying with different combinations.
The space between words should be about three times
the average space between letters.
SUGGESTED EXERCISES FOR HOME WORK
Capital Letters
(Make the capital letters jV" high)
A series of par
1. I I I I I l~~ ^^^^ oblique hues
about 1^'' apart.
A series the same
_____^_________________ as No. 1, with the
2. I I I I I T~ addition of the
horizontal line to
form the letter L.
The same as No.
1, with the addi
tional line to make
the letter T.
A series of par
allel lines having
alternate small and
large spaces.
3. //////
4. // // // //
LETTERING 157
Make the small spaces about A" and the large
ones about A " 
A series similar
to No. 4, with the
addition of the
_^ cross line in the
5. /— / /"T /~7 \~~i small spaces to
form the letter H.
Notice that the
cross bar is slightly
above the center.
The same as No.
4, with the addi
tional hne to make
the letter N.
The same as No.
1, with additions
to form the letter
E. Note that the
y —r rr — ~~r. r — upper horizontal
line is shorter than
the lower one, and
that the middle
one is slightly
above the center.
The same as No.
1, with additions
^ I l_ l_ l_ to form the letter
^' i~ r r r ^ This is the let
ter E with the le wer
line omitted.
H
H
H
H
N
N
N
N
t
h
h
h
t
h
h
h
158
MECHANICAL DRAWING
9.
K K hCR
10. 1^ M M M
11
A A A 'T^
12.
Y \y V V
13. ^ ^ w w
The same as No.
1, with the hnes to
form the letter K.
The width of the
M is equal to the
height. Either
form may be used,
although the one
at the right is pre
ferable.
First draw a ser
ies of center hnes
about T&" apart.
About these center
lines construct the
letters. After be
coming familiar
with the relation of
the component
parts, draw a ser
ies without the use
of the center lines.
Follow the gen
eral directions
given for No. 11.
The center lines
of the two parts of
the W should be
about \" apart.
Having drawn the
center hnes, con
LETTERING 159
struct the letter. Finally, draw the letters without
the center lines.
Draw a series of
center Unes as di
rected for No. 11.
The intersection of
the cross lines
should be slightly
above the center of
the letter.
The center hne
of the letter forms
the lower part of
i^. X i X X
15. Y Y Y Y~ the letter Y. The
vertex of the V is
slightly below the
center of the letter.
Draw the con
struction lines as
directed for No. 4.
, Form the letter by
16. / Y / Yl ^^® ^^^ ^^ these
Hues. Finally draw
the letter without
the use of the con
structions.
Draw the con
. , ' struction lines to
117 fjj [J [J [j the directions given
for No. 4. Read
the text given in
160 MECHANICAL DRAWING
connection with Fig. 56, page 155. Follow the di
rections there given. Finally, make the letter with
out the use of the construction lines.
The same con
structions are used
as for the letter 0.
The C is the letter
18 ~fi^ ~n 'M T^ O with a portion
* ^ ^^—^ ^^ at the right left
out. The G is the
letter C with the
additions shown.
The combination
of the lower part
of the letter O with
19. UJ U U U~ straight linesforms
"'^^ the letter U. Use
the same construc
tions as for the let
ter O, No. 17.
The right hand
portion of the let
ter D is the same
as the correspond
ing part of the let
ter O.
Note that the
, / , , loop of the letter
21. H h" H Af "" P is less than one
half of the height
of the letter. The
20 /) /; /; //
LETTERING 161
curve is onehalf of an O, joining horizontal lines.
The R is the letter P with an additional line. Use
spacing given for No. 1.
Note in the letter
B that the upper
loop is smaller than
the lower one.
I This letter is com
22. j^ Jj ^ ^ " posed of curves
' similar to the letter
O, joined to hori
zontal lines. Use
the spacing given
for No. 1.
The letter S,
probably the most
difficult of all the
letters to make, is
one continuous
curve. Consider
able practice will
be required to
make this letter
well. Use the
spacing given for
No. 4.
SMALL LETTERS
Some of the small letters are exactly the same shape
and have the same proportions as the capitals, the
only way of distinguishing them from the capitals
23 H S S S
162 MECHANICAL DRAWING
being by the height. A reference to page 154 will
show that this is true of the letters c, o, s. v, w, x, and
z. The letter 1 is a straight line, resembling the
capital I. The main lines of the t and i are also
straight lines. The small u is similar to the capital
U, only the straight line at the right continues down
below the loop. The letters f, j, k, and r are easily
formed, and require no special directions. The
letters a, b, d, g, p, and q are based upon the letter
o and a straight line tangent. The upper parts of
the loops of the h, m, and n is the curve of the upper
part of the letter o. From this it will be seen that a
perfect mastery of the curves of the letter o is ab
solutely necessary.
SUGGESTED EXERCISES FOR HOME WORK
Small Letters
(Make the body of the small letters " high)
The letter o until
perfectly mastered .
Make the let
24. O O O n — ~ ^^^^ ^'^ ^^^ have
a space of about A''
between each
letter.
The letter o with
the tangent
straight line form
25. CJ CJ n 0~~ ing the letter a.
Many think it bet
ter to draw the
straight line first.
1
26 ^ b b ( T ^ S.
LETTERING 163
The letters b and
d consist of the let
ter o with the
straight line tan
gent. Notice that
the d is shorter
than the b.
The letter o with
the straight line
tangents extending
below the line
r>y — ^ j^ 1^ Y^ — forms the p and q.
'^ '  H H — H W  Notice the sHght
curve at the lower
part of the straight
line of the q.
The small e is
the letter c with
— the horizontal line
— ^ C! S ^ — addition. It is
best to draw the
horizontal line
last.
The loops of the
h and n are the
— ^ ^^^i ^ ^ same as the upper
29. ZT] — rr n f) p^^^ ^f ^^^ ^^^^^^
o. The remaining
parts of the letters
are made up of
straight lines.
164 MECHANICAL DRAWING
The m is similar
30. m m rrr ^ ^^ ^^^ ^^ ^"^^ ^^^
loops are nar
rower.
FIGURES
Copy the series of figures given on page 154, until
a perfect mastery has been obtained.
CHAPTER XV
GEOMETRICAL DEFINITIONS
POINT
A point indicates position only, and has no dimen
sion.
LINES
A line is produced by the motion of a point and has
dimension in length only. (In drawing a line with
a pencil, the successive positions of the pencil point
produce the line.)
Lines may be straight, curved, broken or mixed.
A straight line is a line
which has the same di
rection throughout its en
tire length. See Fig. 57.
quently called a right line.
A curved line is a line no
part of which is straight.
See Fig. 58.
A broken line is a ser
ies of straight lines drawn
in different directions.
See Fig. 59. Fig
Fig. 57
A straight line is fre
166
MECHANICAL DRAWING
Fig. 60
A mixed line is a line composed of straight and
curved lines. See Fig. 60.
Straight lines are often
called simply lines; and
curved lines, curves.
Straight lines may be horizontal, vertical or oblique.
A line drawn from left to right is termed a hori
zontal line. A horizontal
line is shown at A B,
Fig. 61.
Lines drawn in the op
posite direction are called
vertical lines. Line C,
Fig. 61, is a vertical line.
Any straight line neither horizontal nor vertical
is called an oblique line. See lines D 0, Fig. 61.
Parallel lines are everyw^here equally distant from
each other. The lines
shown in Fig. 62, are
Fig. 62 parallel.
A line is perpendicular to another line when it
meets that line so as not to incline towards it on either
\ ^ side. (When speaking of
perpendicular lines, the
relation of one line to
another is always under
stood. Thus, a vertical
line when alone is not a
^^^" ^^ perpendicular and is only
spoken of as such when it is referred to in connection
with a horizontal line. The horizontal and vertical
GEOMETRICAL DEFINITIONS
167
lines in Fig. 61 are perpendicular, which is equally
true of the two lines shown in Fig. 63.)
ANGLES
The opening between two straight lines which
meet is called an angle. The lines M R and M N,
Fig. 64, form an angle. ^
The lines are called the
sides of the angle, and
the point of meeting is
known as the vertex.
The size of an angle ^
depends, not upon the
length of its sides, but upon the amount of the open
ing between the sides.
When the sides of an angle are drawn in opposite
directions they form a
straight angle. Lines
A
drawn in opposite di ^^^ ^^
rections from the point
A
A, Fig. 65, form a
straight angle.
A right angle is formed
when the sides are per ^
S
C
pendicular. The angles ^
^IG. 66
A B C and A B D, Fig.
^^^
66, are right angles.
Every angle less than ^^„^
^^^^^ \
a right angle is an acute ^^^""^^
angle. See Fig. 67. i
^iG. 67
168
MECHANICAL DRAWING
Fig. 68
When an angle is greater than a right angle and
less than a straight angle,
the a n g l«e formed is
called an obtuse angle.
See Fig. 68.
An angle greater than
a straight angle and less
than two straight angles
is called a reflex angle.
Fig. 69 represents a re
flex angle.
Two angles are com
plementary when their
sum is equal to a right
angle. Each is called
the complement of the
other. In Fig. 70, the
angles L N and M O
N are complementary.
When the sum of two
angles is equal to a
straight angle, the angles
are called supplementary,
and each is called the
supplement of the other. The angles W X Y and
W X Z, Fig. 71, are supplementary.
TRIANGLES
A triangle is a plane surface bounded by three
straight lines. The bounding lines are called the
sides of the triangle, the angles formed by the sides
GEOMETRICAL DEFINITIONS
169
Fig. 72
are called the angles of the triangle and the vertices
of these angles are the vertices of the triangle. The
base of a triangle is the
side upon which it is sup
posed to stand. The
angle opposite the base
is known as the vertical
angle, and the vertex of
this angle is called the
vertex of the triangle.
The altitude of a tri
angle is the perpendicu
lar distance from the
vertex to the base or the
base produced. See line
A B, Figs. 72 and 73.
Fig. 73
Triangles classified hy sides
An equilateral triangle is one having all of its sides
equal in length. See
Fig. 74. This triangle
is frequently called equi
angular, as all of its
angles are also equal.
An isosceles triangle is
one having two of its
sides equal. See Fig. 75.
Two of the angles of an
isosceles triangle are also
equal.
A scalene triangle is one having no two of its sides
Fig. 74
170
MECHANICAL DRAWING
Fig. 75
Fig. 76
equal. See Fig. 76. None of the angles of a scalene
triangle are equal.
Triangles classified by their angles
A rightangled triangle
or right triangle is one
having a right angle.
See Fig. 77.
Fig. 77
An acuteangled tri
angle is one having three
acute angles. See Fig. 78.
Fig. 78
An obtuseangled tri
angle is one having an
obtuse angle. See Fig. 79.
Fig. 79
GEOMETRICAL DEFINITIONS
171
QUADRILATEKAL
A quadrilateral is a
plane surface bounded by
four straight lines.
A trapezium is a quad
rilateral which has no two
of its sides parallel. See
Fig. 80.
A trapezoid is a quadri
lateral having two and
only two of its sides par
allel. See Fig. 81.
A parallelogram is a
quadrilateral having its
opposite sides parallel.
There are four kinds of
parallelograms: the rec
tangle, the square, the rhomboid,
and the rhombus.
A rectangle is a parallelogram
whose angles are all right angles.
Rectangles are shown in Figs. 82
and 83.
A square is a rectangle all of
whose sides are equal. See Fig. 83.
A rhomboid is a par
allelogram whose angles
are not right angles.
Figs. 84 and 85 represent
rhomboids.
Fig. 82
Fig. 83
172 MECHANICAL DRAWING
Fig. 85
A rhombus is a rhom
boid all of whose sides
are equal. See Fig. 85.
POLYGONS
A polygon is a plane surface bounded by straight
lines. This term is usually applied to figures hav
ing more than four sides. The number of sides de
termines the name of the polygon.
A polygon of five sides is called a pentagon; one of
six sides is a hexagon, one of seven sides is a heptagon,
one of eight sides is an octagon, one of nine sides is a
nonagon, and one of ten sides is a decagon.
A regular polygon has all of its sides and all of its
angles equal.
A polygon is irregular when either sides or angles
are unequal.
CIRCLE
A circle is a plane figure
bounded by a curved line called
the circumference, every point
of which is equidistant from
a point within called the center.
See Fig. 86.
The radius of a circle is a
straight line drawn from the
center to a point in the cir ^^^ ^^
GEOMETRICAL DEFINITIONS
173
Fig. 87
The arc
cumference. Line A B, Fig. 87, is a radius. All
the radii of a circle are equal.
The diameter of a circle is a straight line drawn
through the center and
joining two points in the
circumference. Line C
Dj Fig. 87, is a diameter.
A diameter is equal to
two radii.
i An arc of a circle is any
'part of its circumference,
as E K H, Fig. 87. An
, arc equal to onehalf of the
i circumference is called a semicir cumference.
' C K D, Fig. 87, is a semicir cumference.
A chord is a straight hne joining the extremities
> of an arc. See hne E H, Fig. 87.
A tangent is a straight
line which touches the cir
cumference of a circle but
does not intersect it, as
M N, Fig. 87. The point
at which the tangent
touches the circle is called
the point of tangency.
The tangent is always
perpendicular to the ra
dius at the point of tan
gency.
A segment of a circle is the area bounded by an arc
cand its chord. See Fig. 88. A segment equal to
Fig. 88
174
MECHANICAL DRAWING
onehalf the circle is called a semicircle. See R V T O,
Fig. 88.
A sector is the area bounded by two radii and the
arc which they meet. See Fig. 88. When the radii
are perpendicular, the sector equals onefourth of
a circle and is called a quadrant. See R Y, Fig. 88.
Every circle is supposed to be divided into 360
parts^ called degrees, which are used as a measurement
for angles. An arc of a semicircle^ or straight angle,
is equal to 180 degrees. An arc of a quadrant, or
right angle, is equal to 90 degrees.
SOLIDS
A polyhedron is a solid bounded by planes. The
bounding planes are the faces, and their intersections
are the edges of the polyhedron.
Polyhedrons are classified according to the shape
and relation of their faces.
Prisms
A prism is a polyhedron
of which two opposite par
allel faces, called bases, are
equal and parallel poly
gons, and the other faces,
called lateral faces, are par
allelograms. See Figs. 89
and 90. The intersections
of the lateral faces of a
prism are called lateral
edges.
The altitude of a prism is the perpendicular dis
tance between the bases.
Fig. 89
GEOMETRICAL DEFINITIONS
175
A right prism is one whose lateral edges are per
pendicular to the bases. See Fig. 89.
A regular prism is a
right prism whose bases
are regular polygons.
An oblique prism is one
whose lateral edges are
not perpendicular to the
bases. See Fig. 90.
A truncated prism is the
part remaining between
the base and a cutting
Fig. 90
plane oblique to the base
which intersects all of the
lateral edges. A trun
cated prism is shown in
Fig. 91.
Prisms are named by
their bases. They are
triangular, square, rec
FiG. 9i. tangular, hexagonal, etc.,
as the bases are triangles, square, rectangles, hex
agons, etc.
Pyramids
A pyramid is a polyhedron one face of which,
called the base, is a polygon and whose lateral faces
are triangles whose vertices meet in a common point
called the vertex of the pyramid. See Fig. 92.
The altitude of a pyramid is the perpendicular dis
tance between the base and the vertex.
176
MECHANICAL DRAWING
Fig. 92
A regular pyramid is a
pyramid whose base is a
regular polygon the center
of which is in a perpen
dicular to the base let fall
from the vertex.
A pyramid is triangu
lar, pentagonal, octogonal,
etc., as its base is a tri
angle, a pentagon, an oc
tagon, etc.
The frustrum of a pyramid is the portion remaining
between the base and a
cutting plane parallel to
the base which cuts all of
the lateral edges. See
Fig. 93.
The altitude of the frus
trum of a pyramid is the
perpendicular distance between the base and the cut
ting plane parallel to the base.
Cylinders
A cylindrical surface is a
curved surface generated
by a moving straight line
which constantly touches
a given curve, and moves
so that any two positions
are parallel. See Fig. 94.
In this figure, if the line
A B moves parallel to the
Fig. 93
GEOMETRICAL DEFINITIONS
177
position lettered and is constrained to follow the
curve A E H, a cylindrical
surface is produced. Any
position of this moving
line, E F, parallel to A B,
Fig. 94, is called an ele
ment of the surface.
A cylinder is a solid
bounded by a cylindrical
surface and two parallel ^^^' ^^
planes, called bases. See Figs. 95 and 96.
A right cylinder is one whose elements are per
pendicular to the bases.
^""^ "^"^ See Figs. 95 and 96.
When the elements
of the cylindrical sur
face are not at right
angles to the bases, the
cylinder is called an ob
lique cylinder.
A circular cylinder is
a cylinder whose bases
are circles. See Fig. 96.
The altitude of a cylinder is the perpendicular dis
tance between the planes of its bases.
Cones
Fig. 96
A conical surface is a curved surface generated by a
moving straight line one point of which is fixed while
the line is made to follow a given curve. In Fig. 97,
178
MECHANICAL DRAWING
the line A B in its several positions passes through the
fixed point A at the same
time touching the curve
BCD.
Any position of the
moving line is called an
element of the conical
surface. Lines A B, A C,
and A D, Fig. 97, are ele
ments of the surface.
Fig. 9
The fixed point through which the elements pass is
called the vertex.
A cone is a solid bounded
by a conical surface and a
plane surface cutting all the
elements of the conical sur
face. See Fig. 98.
The altitude of a cone is
the perpendicular distance
between the vertex and the
plane of the base. ^^^ ^^
A circular cone is one whose base is a circle.
A right circular cone is a
circular cone whose vertex
_ lies in a line drawn per
pendicular to the plane of
the base from its center.
The frustrum of a cone
is the part contained be
tween the base and a cutting plane parallel to the
base. See Fig. 99.
GEOMETRICAL DEFINITIONS 179
The altitude of a frustrum is the perpendicular
distance between the base and the cutting plane
parallel to the base.
Sphere
A sphere is a solid bounded by a curved surface
every point of which is equidistant from a point
within called the center.
The radius of a sphere is the straight line drawn
from the center to the bounding surface. All radii
are equal.
The diameter of a sphere is a straight line drawn
through the center and terminating in the spherical
surface. The diameter is equal to two radii.
CHAPTER XVI
GEOMETRICAL PROBLEMS
In the figures accompanying these problems, the
given Hnes are made heavy and full, the required
lines are made heavy with a long and short dash,
and the construction lines are made full, light lines.
GEOMETRICAL PROBLEMS
181
PROBLEM 1
To bisect a straight line
— With the ends A and B
as centers and a radius
greater than onehalf the
length of the line, draw
^ arcs C and D intersecting
on each side of the line. A
line drawn through these
intersections will bisect and
be perpendicular to the
given line.
PROBLEM 2
To bisect an arc — Draw
the chord of the arc and
bisect this chord. This
bisector will biseqt the arc
and will pass through the
center about which the
arc is drawn.
PROBLEM 3
To draw a perpendicular
to a line from a point near
the center of the line —
Using the given point A as
a center, with any radius
draw arcs 1 and 2, cutting
the given line at B and C.
With these points of inter
section as centers, draw the
182
MECHANICAL DRAWING
arcs D and E. A line drawn from the point of in
tersection of these arcs to the point A will be per
pendicular to the given line.
PROBLEM 4
To draw a perpendicular to
a line from a point at or near
the end of the line — With
any radius and the given
point A as a center, draw
arc intersecting the given
line at B. With B as a center
and the same radius, draw
arc 2 cutting arc 1 at the
point C. With C as a center
and the same radius, draw
arc 3, cutting arc 1 at D.
With D as a center and the
same radius, draw arc 4 cutting arc 3 at E. A line
drawn from E to A will be perpendicular to the given
line.
PROBLEM 5
To draw a perpendicular to a
line from a point outside of
and near the end of the line
— Through the given point
A draw any line, such as A
B, intersecting the given
line. Find the point C by
bisecting the line A B. (See
Problem 1.) Draw the semi
GEOMETRICAL PROBLEMS
183
circle A B D with C as a center. A line connecting
A and D will be perpendicular to the given line.
PROBLEM 6
To draw a perpendicular to
a line from a point outside of
and near the center of the
line — With the given point
A as a center with any ra
dius, draw arc 1, intersect
ing the given line at B and
C. With points B and C
as centers and equal radii,
draw arcs 2 and 3, inter
secting at D. The line A
D is the required perpen
dicular.
PROBLEM 7
To draw a line through a
given point parallel to a
given line — With the given
point A as a center with
any radius, draw arc 1, in
tersecting the given line at
B. With B as a center with
the same radius, draw arc
2 through A intefrsecting
the given line at C. With
a radius equal the distance
184
MECHANICAL DRAWING
C A and B as a center, draw arc 3, intersecting arc 1
at D. A line drawn through A and D will be par
allel to the given line.
PROBLEM 8
To divide a straight line into
any number of equal parts —
At any angle with the given
line, A B, draw an indefinite
line A C. Lay off on this
line the required number of
equal spaces. Through the
points thus obtained draw
a series of lines parallel to
a line connecting the last
point and the end of the line
to be divided. (See Prob
lem 7.) In the accompany
ing figure, the line A B is
to be divided into five equal
parts. On A C five equal
spaces are laid off. Lines
drawn through points 1, 2,
3, and 4 parallel to a line
connecting B and 5 will
divide the line A B into
five equal parts.
PROBLEM 9
Upon a straight line to construct an angle equal to a
GEOMETRICAL PROBLEMS
185
given angle — Let A B C be
the given angle and D E
the given line. With B as
center and anyradius, draw
arc 1, cutting the side of the
angle at F and G. With D
as a center and with the
same radius, draw arc 2,
cutting D E at H. With
F as a center, draw arc 3
through G. With the same
"c" radius and with H as a
center, draw arc 4 cutting
arc 2 at K. Angle K D H
will equal angle ABC.
PROBLEM 10
To bisect an angle — With
A as a center and any
radius, draw an arc, inter
secting the sides of the
angle at B and C. With
B and C as centers and
equal radii, draw arcs, in
tersecting at D. Line D
A will bisect the angl'e
B A C.
186
MECHANICAL DRAWING
PROBLEM 11
To construct an equilateral
triangle on a given base, —
The line A B is the given
base. With A as a center,
draw arc 1 through B.
With B as a center, draw
arc 2 through A and inter
secting arc 1 at C. Lines
C A and C B complete the
triangle.
PROBLEM 12
To construct an isosceles
triangle on a given base,
having given the length of the
equal sides — The line A B is
the given base and C D is
the length of the equal
sides. With the ends of
the line A B as centers and
a radius equal to the length
of the line C D, draw arcs
intersecting at E. The
lines A E and B E com
plete the required isosceles
triangle.
GEOMETRICAL PROBLEMS
187
PROBLEM 13
To construct a scalene
triangle, the length of the
sides being given — Let A
B, C D, and E F be the
length of the sides. With
A as a center and the
length of the side C D as
a radius, draw arc 1.
With B as a center and
a radius equal to the
length of the side E F,
draw arc 2, intersecting
arc 1 at H. Lines H A
and H B complete the re
quired scalene triangle.
PROBLEM 14
To construct a square,
the length of the sides be
ing given — The line A B
is the length of one side
of the square. Erect a
perpendicular to A B at
the point B. (Problem
4.) With B as a center,
draw an arc through A,
cutting line B C at C.
With A and C as centers
and the same radius,
188
MECHANICAL DRAWING
draw arcs 4 and 2 intersecting at D.
and C D complete the required square.
Lines A D
PROBLEM 15
To circumscribe a circle
about a triangle — Bisect two
of the sides of the triangle,
as A B and B C. (Problem
1.) With the intersection
of these bisectors, point D,
as a center, draw an arc
through point A. This
will be an arc of a circle
passing through A, B, and C.
B PROBLEM 16
To circumscribe a circle
about a square — Draw the di
agonals A C and B D inter
secting at E. With E as a
center and radius E B, draw
the circumscribing circle.
PROBLEM 17
To inscribe a circle within
a triangle — Bisect two of
the angles. (Problem 10.)
Through D, the intersec
tion of these bisectors,
draw D E perpendicular to
A C. (Problem 6.) With
D as a center and radius
D E, draw the required
inscribed circle.
GEOMETRICAL PROBLEMS
189
PROBLEM 18
To draw a tangent to a
circle at a given point on the
circumference — T h r o u g h
the given point A, draw
the radial line A C. Erect
a perpendicular to A C at
the point A. (Problem 4.)
The perpendicular A B is
the required tangent at A,
and the point A is the point
of tangency.
PROBLEM 19
To draw a tangent to an
arc at a point on the arc,
when the center is not
known — With the given
point A as a center, draw
arcs 1 and 2, cutting the
arc at B and C. Draw
the chord B C. Through
the point A draw a line
parallel to B C. (Prob
lem 7.) This line will be
tangent to the arc at the
point A.
PROBLEM 20
To draw a tangent to a circle from a point outside the
190
MECHANICAL DRAWING
circle — From the given point
A draw a line to the center
of the circle. Find point
B by bisecting the line A C.
(Problem 1.) With B as
a center and radius B A,
draw semicircle 1, intersect
ing the circle at D. The
line DA will be tangent to
the circle at D.
Note. — If from any point on
the arc of a semicircle lines be
drawn to the ends of the diameter,
the included angle will be a right
angle. In the figure, the angles
A C B, A D B and A E B are right
angles.
PROBLEI^ 21
To draw an arc of a given
radius tangent to two con
verging lines— Let A B and
C D be the converging lines
and E F the given radius.
At any points, I and J, draw
perpendiculars to A B
and C D. (Problem 4.)
Make I G and J H equal to
E F. Draw H K and G L
GEOMETRICAL PROBLEMS
191
parallel to the lines C D and A B. (Problem 7.)
From M draw M S and M T perpendicular to A B
and C D. (Problem 6.) With M as a center and
radius M T, draw the required arc tangent to the
converging lines at S and T.
PROBLEM 22
To draw an arc of a given
radius tangent to two circles
of fixed diameters — Let C
D be the given radius.
From A and B, the centers
of the given circles, draw
any indefinite lines A K
and B L. Make G K and
H L equal to C D. With
B as a center and radius
B L, draw arc 1. With
A as a center and radius
A K, draw arc 2 intersect
ing arc 1 at M. M is the
center of the required tan
gent arc. Lines M A and
M B will determine points
of tangency T and S.
PROBLEM 23
To draw an arc of a given radius tangent to a given
line and arc — Let A B be the given radius, C D the
given line and E H S the given arc. Draw any radial
192
MECHANICAL DRAWING
line G H. Measure off H K
equal to A B. With G as a
center and radius G K, draw
arc 1. Draw line L M par
allel to and a distance equal
to A B from C D. (Prob
lems 7 and 21.) Where LM
cuts arc 1, draw N T per
pendicular to C D. (Prob
lem 6.) With N as a center
and radius N T^ draw the re
quired tangent arc. T is
one point of tangency^ and
the other one may be ob
tained by extending G N
to S.
PROBLEM 24
To construct an angle of 6o
degrees — Let A B be one
of the sides. With A as a
center and any radius, draw
arc 1, cutting A B at C.
With C as a center and
the same radius, draw arc
2 cutting arc 1 at D. Line
iS A D will make an angle of
60 degrees with A B.
GEOMETRICAL PROBLEMS
193
PROBLEM 25
To construct an angle of
30 degrees — The line A B
is one of the sides. With
any point X as a center
and radius X A, draw a
semicircle cutting the line
A B at C. With C as a
center and the same radius,
draw arc 2 cutting arc 1
at D. AD will make an
angle of 30 degrees with
AB.
PROBLEM 26
To draw a hexagon, hav
ing given the long diameter
— Let A B be the long di
ameter. Find point C by
bisecting A B. (Problem
L) With C as a center
and radius A C, draw a
circle. With A as a center
and the same radius, draw
arcs 1 and 2, cutting the
circle at D and E. With
B as a center and the same
radius, draw arcs 3 and
4, cutting the circle at G
and F. Lines A D, D G,
G B, B F, F E, and E A
will form a hexagon.
194
MECHANICAL DRAWING
PROBLEM 27
To draw a hexagon, when
the length of one side is
given — If A B is the given
side, draw arcs 1 and 2
with A and B as centers
and radius A B. With C
as a center, draw circle 3
through A and B. With
D as a center, and same
radius, draw arc 4, cutting
circle 3 at F. With E as
a center and the same ra
dius, draw arc 5 cutting
circle at G. Lines A D, D
F, F G, G E, and E B are
the required lines of the
hexagon.
PROBLEM 28
To draw a hexagon, the
short diameter being given
— Erect the perpendiculars
G E and D F at the ends
of the short diameter A B.
(Problem 4.) Find point
C by drawing the bisector
H K. (Problem 1.) Make
angle BCD equal 30 de
grees. (Problem 25.) With
GEOMETRICAL PROBLEMS
195
C as a center and a radius equal to the distance
from C to D, draw a circle. Connecting points D H,
H G, G E, E K, K F, and F D will give the required
hexagon.
PROBLEM 29
£^
^
<^^^
^^^
^
1 1
\
/
\
/
\
//
1
^
^^
^
To draw an octagon, hav
ing given the long diameter
— Find point C by bisect
ing the long diameter A B.
(Problem 1.) Draw lines
F H and K G making
angles of 45 degrees with
A B. (Bisect angles BCD
and A C D.) With C as a
center and a radius equal
to the distance from C to
B draw a circle. Con
necting B F, F D, D K,
K A, A H, H E, E G, and
G B will give the required
octagon.
CHAPTER XVII
GEOMETRICAL EXERCISES
SUGGESTIONS FOR HOME WORK
These problems may be solved in a 5x7 rectangle.
For the home work a cheap compass, made espe
cially for the solution of problems in geometry and
costing about 25 cents, may be employed. If these
problems are inked, it is well to ink all given hnes full,
all results ^dth a long and short dash, and to leave
all construction lines in pencil. Show the construc
tion for each problem entering into the solution of
the exercise.
1. Draw an oblique line Ste'^ long and bisect it.
(Problem 1, page 181.)
2. Bisect an arc of Stg'^ radius, having a chord of
4^'\ (Problem 2, page 181.)
3. Di\dde a horizontal line 4:^'^ long into four equal
parts. (Original.)
4. Divide the arc of a semicircle of 21'^ radius
into four equal parts. (Original.)
5. Locate two points 3W^ apart. Draw an arc
through these points T\dth 3j' radius. (Original.)
6. Draw an oblique line 4F' long. Erect a per
pendicular at a point on the line 2'' from one end.
rProblem 3, page 181.)
GEOMETRICAL EXERCISES 197
7. At a point Y^ from the end of and on a hori
zontal hne 5'^ long, erect a perpendicular to the line.
(Problem 4, page 182.)
8. The two parallel sides of a trapezoid measure
24^' and 3f , respectively. These two sides are
perpendicular to an oblique line It^'' long. Draw
the trapezoid. (Original.)
9. From a point at least 2^^ above and near the
end of a horizontal line 4i'' long, draw a perpendicu
lar to the line. (Problem 5, page 182.)
10. Draw a perpendicular to a horizontal line
which is 3F' long from a point at least 2i'' from and
over the center of the line. (Problem 6, page 183.)
11. Two lines 21^' and 3f long, respectively,
form a right angle. Draw the angle. (Original.)
12. Through a point not less than 1^' from an
oblique line 3F' long draw a parallel to the line.
(Problem 7, page 183.)
13. Draw a parallelogram in which two of the sides
shall be Sye'' long and If" apart. (Original.)
14. Divide a line Aite" long into three equal parts.
(Problem 8, page 184.)
15. Draw two lines making any obtuse angle;
copy the angle; have none of the lines horizontal
and all at least 2i'' long. (Problem 9, page 184.)
16. Draw any acute angle having sides at least
2f long. Bisect the angle. (Problem 10, page
185.)
17. Bisect a right angle having sides at least 2rf
long. (Original.)
18. Draw any obtuse angle with sides at least
198 MECHANICAL DRAWING
2i'' long. Divide the angle into four equal parts.
(Original.)
19. An oblique line 2W long is the base of an
equilateral triangle. Construct the triangle. (Prob
lem 11, page 186.)
20. A vertical line 3i'' long is one side of an
equiangular triangle. Draw the triangle. (Original.)
21. Draw an isosceles triangle in which the base
is a horizontal line 3A'' long and the equal sides are
2^'\ (Problem 12, page 186.)
22. The altitude of an isosceles triangle is 3W
and the base is 2 J''. Draw the triangle. (Original.)
23. Draw an isosceles triangle in which the equal
sides are 2f long and form a right angle. (Orig
inal.)
24. Construct a scalene triangle having sides
2¥\ 3V' and 4^'. (Problem 13, page 187.)
25. The base of a scalene triangle is 3F' long.
One of the other sides makes a right angle with the
base and the third side is 5i'' long. Draw the tri
angle. (Original.)
26. The altitude of a triangle is 21''; the base
is 3f long; and one of the sides is 4:W Draw the
triangle. (Original.)
27. Draw a square having sides 3 A^' long. (Prob
lem 14, page 187.)
28. In a rectangle the parallel sides are 3F' and
2f , respectively. Draw the rectangle. (Original.)
29. The three sides of a triangle measure 4f ,
3F' and 3 J''. Circumscribe a circle about this
triangle. (Problem 15, page 188.)
GEOMETRICAL EXERCISES 199
30. Locate any three points and draw a circle
through them. (OriginaL)
31. Circumscribe a circle about a rightangled,
scalene triangle. The base of the triangle is 3i'' and
the altitude is 2" . (Original.)
32. About a three inch square circumscribe a
circle. (Problem 16, page 188.)
33. Within a circle of Z\" diameter draw a square
with the corners touching the circumference of the
circle. (Original.)
34. Inscribe a circle within a square having sides
?>\" long. (Original.)
35. Inscribe a circle within a right triangle having
sides bounding the right angle which measure ^\"
and Z\". (Problem 17, page 188.)
36. At any point on the circumference of a circle
34'' in diameter, draw a tangent to the circle.
(Problem 18, page 189.)
37. Without using the radius of the circle, draw
a tangent to an arc of ?>\" radius. (Problem 19,
page 189.)
38. From a point 3f from the center of a circle
which is Vi' in diameter, draw a tangent to the
circle. (Problem 20, page 189.)
39. Draw two tangents to an arc of 2f radius
from a point M' from the center of the arc. (Origi
nal.)
40. Construct any rightangled triangle the long
est side of which shall be W long. (See note fol
lowing Problem 20, page 190.)
41. Draw two intersecting lines making any angle.
200 MECHANICAL DRAWING
With a radius of IJ^' draw an arc tangent to the
two lines. (Problem 21, page 190.)
42. Two circles of 2\" and ?i\" diameter have
their centers ?>\" apart. With a radius of \\" ,
draw an arc tangent to the two circles. (Problem
22, page 191.)
43. Draw two circles each having a radius of Ir^"
tangent to each other and also tangent to a circle
2\" in diameter. (Original.)
44. Having given three circles 2W 2'^' and 3"
in diameter, draw them so that each shall be tangent
to the other two. (Original.)
45. At a point \\' from one end of a line which
is 4i'' long, erect a perpendicular. At)out a point
on this perpendicular 2^' from the given hne draw
a circle of \\" radius. With a radius of Y^' draw
an arc tangent to the circle and the given straight
line. (Problem 23, page 191.)
46. Using the circle and the straight line described
in Exercise 45, draw an arc of \" radius tangent to
the circle and the straight line with its center out
side of the given circle. (Original.)
47. Construct an angle of 60°, making the sides
at least 2^' long. (Problem 24, page 192.)
48. A vertical line 2\" long forms one side of an
angle of 30°. Construct the angle. (Problem 25,
page 193.)
49. Draw an angle of 30°, without using the method
described in Problem 25. (Combine Problem 24,
page 192 and Problem 10, page 185.)
50. Construct an angle of 15° with one side a
GEOMETRICAL EXERCISES 201
horizontal line not less than 2J'' long. (Orig
inal.)
51. Draw an angle of 224°. Make sides 2i"
long. (Original.)
52. Construct an angle of 75°. (Original.)
53. Draw an angle of 37i°. (Original.)
54. The base of a right triangle is 3f long and one
of the angles is 30°. Draw the triangle. (Original.)
55. In an isosceles triangle the base measures 34''
and the equal angles are 45°. Draw the triangle.
(Original.)
56. The obtuse angle of a scalene triangle measures
135° and the base is 3'' long. Draw a triangle satis
fying these requirements. (Original.)
57. The angle made by the equal sides of an isos
celes triangle is 15° and the equal sides are 4'' long.
Draw the triangle. (Original.)
58. The long diameter of a hexagon is 4''. Con
struct the hexagon. (Problem 26, page 193.)
59. Divide a circle of If radius into six equal
parts. (Original.)
60. Using a line 1^ long as one side of a hexagon,
construct the hexagon. (Problem 27, page 194.)
61. Draw a hexagon having a short diameter of
31''. (Problem 28, page 194.) .
62. Draw a polygon having a long diameter of
3" and twelve equal sides. (Original.)
63. Draw an octagon with the long diameter 4i".
(Problem 29, page 195.)
64. Inscribe a circle within an octagon whose
circumscribing circle is Irl" radius. (Original.)
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